Partitioning Medical Binary Decision Diagrams for Size Optimization

ABSTRACT

In particular embodiments, a method includes accessing a first binary decision diagram (BDD) representing data streams from sensors, selecting portions from the first BDD, constructing a second BDD representing the selected portions and a third BDD representing the non-selected portions, determining sizes of the first, second, and third BDDs, and if the size of the first BDD is less than a sum of the sizes of the second and third BDDs, then storing the first BDD, else storing the second and third BDDs.

TECHNICAL FIELD

This disclosure generally relates to sensors and binary decisiondiagrams, and in particular for monitoring and analyzing a person'shealth.

BACKGROUND

A sensor network may include distributed autonomous sensors. Uses ofsensor networks include but are not limited to military applications,industrial process monitoring and control, machine health monitoring,environment and habitat monitoring, utility usage, healthcare andmedical applications, home automation, and traffic control. A sensor ina sensor network is typically equipped with a communications interface,a controller, and an energy source (such as a battery).

A sensor typically measures a physical quantity and converts it into asignal that an observer or an instrument can read. For example, amercury-in-glass thermometer converts a measured temperature intoexpansion and contraction of a liquid that can be read on a calibratedglass tube. A thermocouple converts temperature to an output voltagethat a voltmeter can read. For accuracy, sensors are generallycalibrated against known standards.

A binary decision diagram (BDD) is a data structure that may be used torepresent a Boolean function. A reduced ordered binary decision diagram(ROBDD) is an optimized BDD that has no redundant nodes and isomorphicsub-graphs and that the variables appear in the same order along eachpath from root to a terminal node.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example sensor network.

FIG. 2A illustrates an example data flow in a sensor network.

FIG. 2B illustrates an example sensor.

FIG. 3A illustrates a BDD that represents a Boolean function that hasthree variables.

FIG. 3B illustrates an optimized BDD that represents a Boolean functionthat has three variables.

FIG. 4 illustrates an example data stream.

FIG. 5 illustrates an example method for combining medical binarydecision diagrams for analysis optimization.

FIG. 6 illustrates an example method for partitioning medical binarydecision diagrams for analysis optimization.

FIG. 7 illustrates an example method for combining medical binarydecision diagrams for size optimization.

FIG. 8 illustrates an example method for partitioning medical binarydecision diagrams for size optimization.

FIG. 9 illustrates an example method for combining medical binarydecision diagrams to determine if data is related.

FIG. 10 illustrates an example method for partitioning medical binarydecision diagrams to determine if data is related.

FIG. 11 illustrates an example graph measuring BDD compression rateversus the number of samples represented by the BDD.

FIG. 12 illustrates an example method for performing a compressionthreshold analysis on binary decision diagrams.

FIG. 13 illustrates an example method for detecting sensor malfunctionsusing compression analysis of binary decision diagrams.

FIG. 14 illustrates an example method for detecting data corruption inmedical binary decision diagrams using hashing techniques.

FIG. 15 illustrates an example method for querying data within aspecified range in binary decision diagrams.

FIG. 16 illustrates an example method for annotating medical binarydecision diagrams with health state information.

FIG. 17 illustrates an example computer system.

FIG. 18 illustrates an example network environment.

DESCRIPTION OF EXAMPLE EMBODIMENTS Sensor Networks

FIG. 1 illustrates an example sensor network 100. Sensor network 100comprises a sensor array 110, an analysis system 180, and display system190. Sensor network 100 enables the collecting, processing, analyzing,sharing, visualizing, displaying, archiving, and searching of sensordata. The data collected by sensors 112 in sensor array 110 may beprocessed, analyzed, and stored using the computational and data storageresources of sensor network 100. This may be done with both centralizedand distributed computational and storage resources. Sensor network 100may integrate heterogeneous sensor, data, and computational resourcesdeployed over a wide area. Sensor network 100 may be used to undertake avariety of tasks, such as physiological, psychological, behavioral, andenvironmental monitoring and analysis.

A sensor array 110 comprises one or more sensors 112. A sensor 112receives a stimulus and converts it into a data stream. The sensors 112in sensor array 110 may be of the same type (e.g., multiplethermometers) or various types (e.g., a thermometer, a barometer, and analtimeter). A sensor array 110 may transmit one or more data streamsbased on the one or more stimuli to one or more analysis systems 180over any suitable network. In particular embodiments, a sensor 112'sembedded processors may perform certain computational activities (e.g.,image and signal processing) that could also be performed by othercomponents of sensor network 100, such as, for example, analysis system180 or display system 190.

As used herein, a sensor 112 in a sensor array 110 is described withrespect to a subject. Therefore, a sensor 112 may be personal or remotewith respect to the subject. Personal sensors receive stimuli that arefrom or related to the subject. Personal sensors may include, forexample, sensors that are affixed to or carried by the subject (e.g., aheart-rate monitor, an input by the subject into a smart phone), sensorsthat are proximate to the subject (e.g., a thermometer in the room wherethe subject is located), or sensors that are otherwise related to thesubject (e.g., GPS position of the subject, a medical report by thesubject's doctor, a subject's email inbox). Remote sensors receivestimulus that is external to or not directly related to the subject.Remote sensors may include, for example, environmental sensors (e.g.,weather balloons, stock market ticker), network data feeds (e.g., newsfeeds), or sensors that are otherwise related to external information. Asensor 112 may be both personal and remote depending on thecircumstances. As an example and not by way of limitation, if thesubject is a particular person, a thermometer in a subject's home may beconsidered personal while the subject is at home, but remote when thesubject is away from home. As another example and not by way oflimitation, if the subject is a particular home, a thermometer in thehome may be considered personal to the home regardless of whether aperson is in the home or away.

Analysis system 180 may monitor, store, and analyze one or more datastreams from sensor array 110. Analysis system 180 may havesubcomponents that are local 120, remote 150, or both. Display system190 may render, visualize, display, message, and publish to one or moreusers based on the output of analysis system 180. Display system 190 mayhave subcomponents that are local 130, remote 140, or both.

As used herein, the analysis and display components of sensor network100 are described with respect to a sensor 112. Therefore, a componentmay be local or remote with respect to the sensor 112. Local components(i.e., local analysis system 120, local display system 130) may includecomponents that are built into or proximate to the sensor 112. As anexample and not by way of limitation, a sensor 112 could include anintegrated computing system and LCD monitor that function as localanalysis system 120 and local display system 130. Remote components(i.e., remote analysis system 150, remote display system 190) mayinclude components that are external to or independent of the sensor112. As another example and not by way of limitation, a sensor 112 couldtransmit a data stream over a network to a remote server at a medicalfacility, wherein dedicated computing systems and monitors function asremote analysis system 150 and remote display system 190. In particularembodiments, each sensor 112 in sensor array 110 may utilize eitherlocal or remote display and analysis components, or both. In particularembodiments, a user may selectively access, analyze, and display thedata streams from one or more sensors 112 in sensor array 110. This maybe done, for example, as part of running a specific application or dataanalysis algorithm. The user could access data from specific types ofsensors 112 (e.g., all thermocouple data), from sensors 112 that measurespecific types of data (e.g., all environmental sensors), or based onother criteria.

Although FIG. 1 illustrates a particular arrangement of sensor array110, sensors 112, analysis system 180, local analysis system 120, remoteanalysis system 150, display system 190, local display system 130,remote display system 140, and network 160, this disclosure contemplatesany suitable arrangement of sensor array 110, sensors 112, analysissystem 180, local analysis system 120, remote analysis system 150,display system 190, local display system 130, remote display system 140,and network 160. As an example and not by way of limitation, two or moreof sensor array 110, sensors 112, analysis system 180, local analysissystem 120, remote analysis system 150, display system 190, localdisplay system 130, and remote display system 140 may be connected toeach other directly, bypassing network 160. As another example, one ormore sensors 112 may be connected directly to communication network 160,without being part of a sensor array 110. As another example, two ormore of sensor array 110, sensors 112, analysis system 180, localanalysis system 120, remote analysis system 150, display system 190,local display system 130, and remote display system 140 may bephysically or logically co-located with each other in whole or in part.Moreover, although FIG. 1 illustrates a particular number of sensorarrays 110, sensors 112, analysis systems 180, local analysis systems120, remote analysis systems 150, display systems 190, local displaysystems 130, remote display systems 140, and networks 160, thisdisclosure contemplates any suitable number of sensor arrays 110,sensors 112, analysis systems 180, local analysis systems 120, remoteanalysis systems 150, display systems 190, local display systems 130,remote display systems 140, and networks 160. As an example and not byway of limitation, sensor network 100 may include multiple sensor arrays110, sensors 112, analysis systems 180, local analysis systems 120,remote analysis systems 150, display systems 190, local display systems130, remote display systems 140, and networks 160.

This disclosure contemplates any suitable network 160. As an example andnot by way of limitation, one or more portions of network 160 mayinclude an ad hoc network, an intranet, an extranet, a virtual privatenetwork (VPN), a local area network (LAN), a wireless LAN (WLAN), a widearea network (WAN), a wireless WAN (WWAN), a metropolitan area network(MAN), a portion of the Internet, a portion of the Public SwitchedTelephone Network (PSTN), a cellular telephone network, or a combinationof two or more of these. Network 160 may include one or more networks160. Similarly, this disclosure contemplates any suitable sensor array110. As an example and not by way of limitation, one or more portions ofsensor array 110 may include an ad hoc network, an intranet, anextranet, a VPN, a LAN, a WLAN, a WAN, a WWAN, a MAN, a portion of theInternet, a portion of the PSTN, a cellular telephone network, or acombination of two or more of these. Sensor array 110 may include one ormore sensor arrays 110.

Connections 116 may connect sensor array 110, sensors 112, analysissystem 180, local analysis system 120, remote analysis system 150,display system 190, local display system 130, and remote display system140 to network 160 or to each other. Similarly, connections 116 mayconnect sensors 112 to each other in sensor array 110 (or to otherequipment in sensor array 110) or to network 160. This disclosurecontemplates any suitable connections 116. In particular embodiments,one or more connections 116 include one or more wireline (such as, forexample, Digital Subscriber Line (DSL) or Data Over Cable ServiceInterface Specification (DOCSIS)), wireless (such as, for example, Wi-Fior Worldwide Interoperability for Microwave Access (WiMAX)) or optical(such as, for example, Synchronous Optical Network (SONET) orSynchronous Digital Hierarchy (SDH)) connections. In particularembodiments, one or more connections 116 each include an ad hoc network,an intranet, an extranet, a VPN, a LAN, a WLAN, a WAN, a WWAN, a MAN, aportion of the Internet, a portion of the PSTN, a cellular telephonenetwork, another connection 116, or a combination of two or more suchconnections 116. Connections 116 need not necessarily be the samethroughout sensor network 100. One or more first connections 116 maydiffer in one or more respects from one or more second connections 116.

FIG. 2A illustrates an example data flow in a sensor network. In variousembodiments, one or more sensors in a sensor array 210 may receive oneor more stimuli. The sensor array 210 may transmit one or more datastreams based on the one or more stimuli to one or more analysis systems280 over any suitable network. As an example and not by way oflimitation, one sensor could transmit multiple data streams to multipleanalysis systems. As another example and not by way of limitation,multiple sensors could transmit multiple data streams to one analysissystem.

In particular embodiments, the sensors in sensor array 210 each producetheir own data stream, which is transmitted to analysis system 280. Inother embodiments, one or more sensors in sensor array 210 have theiroutput combined into a single data stream.

Analysis system 280 may monitor, store, and analyze one or more datastreams. Analysis system 280 may be local, remote, or both. Analysissystem 280 may transmit one or more analysis outputs based on the one ormore data streams to one or more display systems 290. As an example andnot by way of limitation, one analysis system could transmit multipleanalysis outputs to multiple display systems. As another example and notby way of limitation, multiple analysis systems could transmit multipleanalysis outputs to one display system. Analysis system 280 may alsostore one or more analysis outputs for later processing.

A display system 290 may render, visualize, display, message, andpublish to one or more users based on the one or more analysis outputs.A display system 290 may be local, remote, or both. In variousembodiments, a sensor array 210 may transmit one or more data streamsdirectly to a display system 290. This may allow, for example, displayof stimulus readings by the sensor.

Although FIG. 2A illustrates a particular arrangement of sensor array210, analysis system 280, and display system 290, this disclosurecontemplates any suitable arrangement of sensor array 210, analysissystem 280, and display system 290. Moreover, although FIG. 2Aillustrates a particular data flow between sensor array 210, analysissystem 280, and display system 290, this disclosure contemplates anysuitable data flow between sensor array 210, analysis system 280, anddisplay system 290.

Sensors

FIG. 2B illustrates an example sensor 212 and data flow to and from thesensor. A sensor 212 is a device which receives and responds to astimulus. Here, the term “stimulus” means any signal, property,measurement, or quantity that may be detected and measured by a sensor212.

In particular embodiments, a sensor 212 receives stimuli from a subject.As an example and not by way of limitation, a subject may be a person(or group of persons or entity), place (such as, for example, ageographical location), or thing (such as, for example, a building,road, airplane, or automobile). Although this disclosure describesparticular types of subjects, this disclosure contemplates any suitabletypes of subjects. In particular embodiments, one or more subjects ofone or more sensors 112 may be a user of other components of sensornetwork 100, such as other sensors 112, analysis system 180, or displaysystem 190. As such, the terms “subject” and “user” may refer to thesame person, unless context suggests otherwise.

A sensor 212 responds to a stimulus by generating a data streamcorresponding to the stimulus. A data stream may be a digital or analogsignal that can be transmitted over any suitable transmission medium andfurther used in electronic devices. As used herein, the term “sensor” isused broadly to describe any device that receives a stimulus andconverts it into a data stream. The present disclosure assumes that thedata stream output from a sensor 212 is transmitted to an analysissystem, unless otherwise specified.

In particular embodiments, one or more sensors 212 each include astimulus receiving element (i.e., sensing element), a communicationelement, and any associate circuitry. Sensors 212 generally are small,battery powered, portable, and equipped with a microprocessor, internalmemory for data storage, and a transducer or other component forreceiving stimulus. However, a sensor 212 may also be an assay, test, ormeasurement. A sensor 212 may interface with a personal computer andutilize software to activate the sensor 212 and to view and analyze thecollected data. A sensor 212 may also have a local interface device(e.g., keypad, LCD) allowing it to be used as a stand-alone device. Inparticular embodiments, a sensor 212 may include one or morecommunication elements that may receive or transmit information (such asdata streams) over a communication channel, for example to one or moreother components in a sensor network.

In particular embodiments, one or more sensors 212 may measure a varietyof things, including physiological, psychological, behavioral, andenvironmental stimulus. Physiological stimulus may include, for example,physical aspects of a person (e.g., stretch, motion of the person, andposition of appendages); metabolic aspects of a person (e.g., glucoselevel, oxygen level, osmolality), biochemical aspects of a person (e.g.,enzymes, hormones, neurotransmitters, cytokines), and other aspects of aperson related to physical health, disease, and homeostasis.Psychological stimulus may include, for example, emotion, mood, feeling,anxiety, stress, depression, and other psychological or mental states ofa person. Behavioral stimulus may include, for example, behavior relateda person (e.g., working, socializing, arguing, drinking, resting,driving), behavior related to a group (e.g., marches, protests, mobbehavior), and other aspects related to behavior. Environmental stimulusmay include, for example, physical aspects of the environment (e.g.,light, motion, temperature, magnetic fields, gravity, humidity,vibration, pressure, electrical fields, sound, GPS location),environmental molecules (e.g., toxins, nutrients, pheromones),environmental conditions (e.g., pollen count, weather), other externalcondition (e.g., traffic conditions, stock market information, newsfeeds), and other aspects of the environment.

As an example and not by way of limitation, particular embodiments mayinclude one or more of the following types of sensors 212:Accelerometer; Affinity electrophoresis; Air flow meter; Air speedindicator; Alarm sensor; Altimeter; Ammeter; Anemometer; Arterial bloodgas sensor; Attitude indicator; Barograph; Barometer; Biosensor;Bolometer; Boost gauge; Bourdon gauge; Breathalyzer; Calorie IntakeMonitor; calorimeter; Capacitive displacement sensor; Capillaryelectrophoresis; Carbon dioxide sensor; Carbon monoxide detector;Catalytic bead sensor; Charge-coupled device; Chemical field-effecttransistor; Chromatograph; Colorimeter; Compass; Contact image sensor;Current sensor; Depth gauge; DNA microarray; Electrocardiograph (ECG orEKG); Electrochemical gas sensor; Electrolyte-insulator-semiconductorsensor; Electromyograph (EMG); Electronic nose; Electro-optical sensor;Exhaust gas temperature gauge; Fiber optic sensors; Flame detector; Flowsensor; Fluxgate compass; Foot switches; Force sensor; Free fall sensor;Galvanic skin response sensor; Galvanometer; Gardon gauge; Gas detector;Gas meter; Geiger counter; Geophone; Goniometers; Gravimeter; Gyroscope;Hall effect sensor; Hall probe; Heart-rate sensor; Heat flux sensor;High-performance liquid chromatograph (HPLC); Hot filament ionizationgauge; Hydrogen sensor; Hydrogen sulfide sensor; Hydrophone;Immunoassay, Inclinometer; Inertial reference unit; Infrared pointsensor; Infra-red sensor; Infrared thermometer; Insulin monitors;Ionization gauge; Ion-selective electrode; Keyboard; Kinestheticsensors; Laser rangefinder; Leaf electroscope; LED light sensor; Linearencoder; Linear variable differential transformer (LVDT); Liquidcapacitive inclinometers; Magnetic anomaly detector; Magnetic compass;Magnetometer; Mass flow sensor; McLeod gauge; Metal detector; MHDsensor; Microbolometer; Microphone; Microwave chemistry sensor;Microwave radiometer; Mood sensor; Motion detector; Mouse; Multimeter;Net radiometer; Neutron detection; Nichols radiometer; Nitrogen oxidesensor; Nondispersive infrared sensor; Occupancy sensor; Odometer;Ohmmeter; Olfactometer; Optode; Oscillating U-tube; Oxygen sensor; Painsensor; Particle detector; Passive infrared sensor; Pedometer;Pellistor; pH glass electrode; Photoplethysmograph; Photodetector;Photodiode; Photoelectric sensor; Photoionization detector;Photomultiplier; Photoresistor; Photoswitch; Phototransistor; Phototube;Piezoelectric accelerometer; Pirani gauge; Position sensor;Potentiometric sensor; Pressure gauge; Pressure sensor; Proximitysensor; Psychrometer; Pulse oximetry sensor; Pulse wave velocitymonitor; Radio direction finder; Rain gauge; Rain sensor; Redoxelectrode; Reed switch; Resistance temperature detector; Resistancethermometer; Respiration sensor; Ring laser gyroscope; Rotary encoder;Rotary variable differential transformer; Scintillometer; Seismometer;Selsyn; Shack-Hartmann; Silicon bandgap temperature sensor; Smokedetector; Snow gauge; Soil moisture sensor; Speech monitor; Speedsensor; Stream gauge; Stud finder; Sudden Motion Sensor; Tachometer;Tactile sensor; Temperature gauge; Thermistor; Thermocouple;Thermometer; Tide gauge; Tilt sensor; Time pressure gauge; Touch switch;Triangulation sensor; Turn coordinator; Ultrasonic thickness gauge;Variometer; Vibrating structure gyroscope; Voltmeter; Water meter;Watt-hour meter; Wavefront sensor; Wired glove.; Yaw rate sensor; andZinc oxide nanorod sensor. Although this disclosure describes particulartypes of sensors, this disclosure contemplates any suitable types ofsensors.

A biosensor is a type of sensor 112 that receives a biological stimulusand converts it into a data stream. As used herein, the term “biosensor”is used broadly.

In particular embodiments, a biosensor may be a device for the detectionof an analyte. An analyte is a substance or chemical constituent that isdetermined in an analytical procedure. For instance, in an immunoassay,the analyte may be the ligand or the binder, while in blood glucosetesting, the analyte is glucose. In medicine, analyte typically refersto the type of test being run on a patient, as the test is usuallydetermining the existence and/or concentration of a chemical substancein the human body.

A common example of a commercial biosensor is a blood glucose monitor,which uses the enzyme glucose oxidase to break blood glucose down. Indoing so, it first oxidizes glucose and uses two electrons to reduce theFAD (flavin adenine dinucleotide, a component of the enzyme) to FADH₂(1,5-dihydro-FAD). This in turn is oxidized by the electrode (acceptingtwo electrons from the electrode) in a number of steps. The resultingcurrent is a measure of the concentration of glucose. In this case, theelectrode is the transducer and the enzyme is the biologically activecomponent.

In particular embodiments, a biosensor combines a biological componentwith a physicochemical detector component. A typical biosensorcomprises: a sensitive biological element (e.g., biological material(tissue, microorganisms, organelles, cell receptors, enzymes,antibodies, nucleic acids, etc.), biologically derived material,biomimic); a physicochemical transducer/detector element (e.g. optical,piezoelectric, electrochemical) that transforms the signal (i.e. inputstimulus) resulting from the interaction of the analyte with thebiological element into another signal (i.e. transducers) that may bemeasured and quantified; and associated electronics or signal processorsgenerating and transmitting a data stream corresponding to the inputstimulus. The encapsulation of the biological component in a biosensormay be done by means of a semi-permeable barrier (e.g., a dialysismembrane or hydrogel), a 3D polymer matrix (e.g., by physically orchemically constraining the sensing macromolecule), or by other means.

In particular embodiments, a sensor 112 may sample input stimulus atdiscrete times. The sampling rate, sample rate, or sampling frequencydefines the number of samples per second (or per other unit) taken froma continuous or semi-continuous stimulus to make a discrete data signal.For time-domain signals, the unit for sampling rate may be 1/s (Hertz).The inverse of the sampling frequency is the sampling period or samplinginterval, which is the time between samples. The sampling rate of asensor 112 may be controlled locally, remotely, or both.

In particular embodiments, one or more sensors 112 in the sensor array110 may have a dynamic sampling rate. Dynamic sampling is performed whena decision to change the sampling rate is taken if the current outcomeof a process is within or different from some specified value or rangeof values. As an example and not by way of limitation, if the stimulusis different from the outcome predicted by some model or falls outsidesome threshold range, the sensor 112 may increase or decrease itssampling rate in response. Dynamic sampling may be used to optimize theoperation of the sensors 112 or influence the operation of actuators tochange the environment.

In particular embodiments, the sampling rate of a sensor 112 may bebased on receipt of a particular stimulus. As an example and not by wayof limitation, an accelerometer may have a default sample rate of 1/s,but may increase its sampling rate to 60/s whenever it measures anon-zero value, and then may return to a 1/s sampling rate after getting60 consecutive samples equal to zero. As another example and not by wayof limitation, if the stimulus measured over a particular range of timedoes vary significantly, the sensor 112 may reduce its sampling rate.

In particular embodiments, the sampling rate of a sensor 112 may bebased on input from one or more components of sensor network 100. As anexample and not by way of limitation, a heart rate monitor may have adefault sampling rate of 1/min, but may increase the its sampling ratein response to a signal or instruction from analysis system 180.

In particular embodiments, one or more sensors 112 in the sensor array110 may increase or decrease the precision at which the sensors 112sample input. As an example and not by way of limitation, a glucosemonitor may use four bits to record a user's blood glucose level bydefault. However, if the user's blood glucose level begins varyingquickly, the glucose monitor may increase its precision to eight-bitmeasurements.

In particular embodiments, the stimulus received by a sensor 112 may beinput from a subject (i.e., the user of the sensor). A subject mayprovide input in a variety of ways. User-input may include, for example,inputting a quantity or value into the sensor, speaking or providingother audio input to the sensor, and touching or providing otherstimulus to the sensor. Any client system with a suitable I/O device mayserve as a user-input sensor. Suitable I/O devices include alphanumerickeyboards, numeric keypads, touch pads, touch screens, input keys,buttons, switches, microphones, pointing devices, navigation buttons,stylus, scroll dial, another suitable I/O device, or a combination oftwo or more of these.

In particular embodiments, a sensor 112 may query the subject to inputinformation into the sensor 112. In one embodiment, the sensor 112 mayquery the subject at static intervals (e.g., every hour). In anotherembodiment, the sensor 112 may query the subject at a dynamic rate. Thedynamic rate may be based on a variety of factors, including prior inputinto the sensor 112, data from other sensors 112 in sensor array 110,output from analysis system 180, etc. As an example and not by way oflimitation, if a heart-rate monitor in sensor array 110 indicates anincrease in the subject's heart-rate, a user-input sensor mayimmediately query the subject to input his current activity.

In particular embodiments, a sensor 112 may be a data feed. A data feedmay be a computing system that receives and aggregates physiological,psychological, behavioral, or environmental data from one or moresources and transmits one or more data streams based on the aggregateddata. Alternatively, a data feed may be the one or more data streamsbased on the aggregated data. As an example and not by way oflimitation, data feeds may be stock-market tickers, weather reports,news feeds, traffic-condition updates, public-health notices, electroniccalendars, data from one or more other users (such as, for example,physiological, psychological, or behavioral data from another user), orany other suitable data feeds. A data feed may contain both personal andremote data, as discussed previously. A data feed may be any suitablecomputing device (such as, for example, computer system 1700).

The example data feeds illustrated and described herein are provided forillustration purposes only and are not meant to be limiting. Thisdisclosure contemplates the use of any suitable data feed.

Data Streams

In particular embodiments, a data stream comprises one or more datatransmitted from one or more sensors 112 in sensor array 110. A datastream may be a digital or analog signal that may be transmitted overany suitable transmission medium and further used in electronic devices.Sensor array 110 may transmit one or more data streams based on one ormore stimuli to one or more analysis systems 180 over any suitablenetwork.

A data stream may include signals from a variety of types of sensors112, including physiological, psychological, behavioral, andenvironmental sensors. A sensor 112 generates a data streamcorresponding to the stimulus it receives. As an example and not by wayof limitation, a physiological sensor (e.g., an accelerometer) generatesa physiological data stream (e.g., an accelerometer data stream, whichincludes, for example, data on the acceleration of a subject over time).

Sensor data may include any suitable information. In particularembodiments, sensor data includes measurements taken by one or moresensors 112. Sensor data may include samples that may have any suitableformat. In particular embodiments, the format of the samples may be atuple (or ordered set) that has one or more data parameters, and aparticular sample may be a tuple of one or more values for the one ormore data parameters. As an example and not by way of limitation, atuple format (t, p) may have data parameters time t and pressure p, anda particular sample (t0, p0) may have values pressure p0 measured attime t0. The tuple format may include any suitable data parameters, suchas one or more sensor parameters and/or one or more test parameters. Asensor parameter may correspond to one or more sensors 112, and a sensorvalue may record one or more measurements taken by one or more sensors112. As an example and not by way of limitation, a sensor value mayrecord a measurement taken by a sensor 112. A test parameter maycorrespond to a factor that describes a temporal, spatial, and/orenvironmental feature of a measurement process, and a test value mayrecord the value of the feature when the measurements are taken. As anexample and not by way of limitation, the parameter may be time and theparameter value may record a particular time at which measurements aretaken.

In particular embodiments, a sensor 112 may transmit one or more data atdiscrete times. The transmitting rate, transmission rate, ortransmitting frequency defines the number of transmissions per second(or per other unit) sent by a sensor to make a discrete data signal. Fortime-domain signals, the unit for transmitting rate may be 1/s (Hertz).The inverse of the transmitting frequency is the transmitting period ortransmitting interval, which is the time between transmissions. Thedatum may be transmitted continuously, periodically, randomly, or withany other suitable frequency or period. This may or may not correlatewith the sampling rate of the sensor.

Reference to sensor data may encompass a sensor data stream, and viceversa, where appropriate. Sensor data may relate to a sensor subject,wherein the sensor 112 receives stimulus from or related to the subject.Sensor data or a data stream may relate to a sensor subject in anysuitable way. As an example and not by way of limitation, sensor datamay relate to a sensor subject because one or more sensors 112 generatedthe sensor data from one or more stimuli produced by the sensor subject.As another example and not by way of limitation, sensor data may relateto a sensor subject because the sensor data may provide insight orfurther understanding of the sensor subject. As yet another example andnot by way of limitation, sensor data may relate to a sensor subjectbecause it may help detect or predict the occurrence of one or moreproblems or events concerning the sensor subject. As yet another exampleand not by way of limitation, sensor data may relate to a sensor subjectbecause it may facilitate monitoring of the sensor subject.

In particular embodiments, the components of sensor network 100 mayutilize some type of data acquisition system to further process the datastream signal for use by analysis system 180. As an example and not byway of limitation, a data acquisition system may convert an analogwaveforms signal into a digital value. As another example and not by wayof limitation, the data acquisition system may convert decimal valuesinto binary values. The data acquisition system may be local, forexample, integrated into a sensor 112 in sensor array 110 or into localanalysis system 120. The data acquisition system may also be remote, forexample, integrated into remote analysis system 150 or an independentsystem.

In particular embodiments, the data acquisition system may perform oneor more signal conditioning processes (for example, if a signal from asensor 112 is not suitable for the type of analysis system 180 beingused). As an example and not by way of limitation, the data acquisitionsystem may amplify, filter, or demodulate the signal. Various otherexamples of signal conditioning might be bridge completion, providingcurrent or voltage excitation to the sensor, isolation, time-basecorrection, and linearization. In particular embodiments, single-endedanalog signals may be converted to differential signals. In particularembodiments, digital signals may be encoded to reduce and correcttransmission errors or downsampled to reduce transmission powerrequirements.

In particular embodiments, the components of sensor network 100 mayutilize some type of data logging system to record, categorize, store,and file data from one or more data streams over time. The data loggingsystem may be local, for example, integrated into a sensor 112 in sensorarray 110 or into local analysis system 120. The data logging system mayalso be remote, for example, integrated into remote analysis system 150or an independent system. The data logging system may also usedistributed resources to record data. The data logging system may storedata on any suitable data store, such as, for example, data store 1840.

The data logging system may record data streams as one or more datasets. A data set comprises one or more data from a data stream. Datasets may be categorized and formed based on a variety of criteria. As anexample and not by way of limitation, a data stream could be recorded asone or more data sets based on the specific subject, sensor, timeperiod, event, or other criteria.

In particular embodiments, one or more data sets from a data stream maybe used to construct a binary decision diagram (BDD) representing thedata sets.

Binary Decision Diagrams

A binary decision diagram is a data structure that may be used torepresent a Boolean function. A BDD may be graphically represented as arooted, directed, and acyclic graph having one or more internal decisionnodes and two terminal nodes. Each decision node represents a differentvariable of the Boolean function, and is typically denoted as a circlein the graph. The two terminal nodes, a 0 terminal node and a 1 terminalnode, are typically denoted as a square each in the graph. Each decisionnode has two edges, a 0 edge, typically denoted as a dash line or adotted line in the graph, and a 1 edge, typically denoted as a solidline in the graph. Each edge may be connected to another decision nodeor to one of the terminal nodes.

Each path in the graph may by formed by one or more decision nodes andtheir associated edges, and eventually leads to either the 0 terminalnode or the 1 terminal node. The decision nodes that form a particularpath each represent a different variable of the Boolean function. Thatis, along a single path, no two decision nodes represent the samevariable. A path that leads to the 0 terminal node indicates that theBoolean function evaluates to FALSE for the values assigned to thevariables represented by the decision nodes on the path, and a path thatleads to the 1 terminal node indicates that the Boolean functionevaluates to TRUE for the values assigned to the variables representedby the decision nodes on the path.

FIG. 3A illustrates an example BDD 300 that represents a Booleanfunction having three variables: x₁, x₂, and x₃. Since the Booleanfunction represented by BDD 300 has three variables, BDD 300 has at mostthree decision-node layers, layers 1, 2, and 3. That is, there are atmost three layers in BDD 300 that each have at least one decision node.The decision node that represents variable x₁ is at layer 1 of BDD 300;the decision nodes that represent variable x₂ are at layer 2 of BDD 300;and the decision nodes that represent variable x₃ are at layer 3 of BDD300. Each path in BDD 100, formed by the decision nodes and theirassociated edges, leads to either the 0 terminal node or the 1 terminalnode, indicating that the Boolean function evaluates to FALSE or TRUE,respectively. Note that for readability, the 0 terminal node and the 1terminal node are duplicated multiple times in FIG. 3A.

A minterm is a logical expression of n variables that employs only thecomplement operator and the conjunction operator. For a Boolean functionof n variables, a minterm is a product term in which each of the nvariables appears once, either in a complemented or uncomplemented form.In particular embodiments, each datum from a data set may be representedas a minterm to yield a set of minterms. A characteristic function maybe generated from the minterms, the characteristic function indicatingwhether a given minterm is a member of the set of minterms.

In particular embodiments, a characteristic function ƒ^(s) ({right arrowover (x)})=1 of a data set S indicates whether a given element(represented by a minterm) is a member of the data set S. As an exampleand not by way of limitation, a data set from a data stream may becharacterized by the Boolean function ƒ^(S)({right arrow over (x)}) of adata set S⊂N , such that f^(s) ({right arrow over (x)})=1 if and only if{right arrow over (x)} is the binary representation of an element ofdata set S. For example, for S={1,3}, f(0,0)=f (1,0)=0 andf(0,1)=f(1,1)=1. Similarly, a plurality of data streams from a pluralityof sensors may also be characterized by a Boolean function. The data setmay comprise a set of tuples of the form S={(t_(i), s_(i) ¹, . . . ,s_(i) ^(k))}, where s_(i) ^(j) is the input from sensor j at timeinstance i. The corresponding Boolean function would be f^(S)({rightarrow over (t)}_(i);{right arrow over (s)}_(i) ¹; . . . ; {right arrowover (s)}_(i) ^(k)). As an example and not by way of limitation, sensorarray 110 may comprise sensor A and sensor B. The data streams fromsensors A and B may be characterized by the Boolean functions ƒ_(A)(t₁,t₂, x₁, x₂, x₃) and ƒ_(B)(t₁, t₂, x₄, x₅, x₆), respectively, where:

(t₁, t₂) is a time associated with a sensor measurement,

(x₁, x₂, x₃) is a measurement by sensor A at a given time, and

(x₄, x₅, x₆) is a measurement by sensor B at a given time.

The Boolean functions ƒ_(A) and ƒ_(B) may be represented by two BDDs,such as BDD_(A) and BDD_(B), respectively. Alternatively, the datastreams from sensors A and B may be characterized by a single Booleanfunction ƒ_(A)(t₁, t₂, x₁, x₂, x₃, x₄, x₅, x₆), which may be representedby a single BDD, such as BDD_(AB).

BDD 300 is not the most optimized representation of the Boolean functionas some of the nodes in BDD 300 are redundant and portions of BDD 300are isomorphic. For example, consider paths 310 and 312, both of whichend at the 0 terminal node. By examining the decision nodes on paths 310and 320, it may be determined that as long as decision node 330, whichrepresents variable x₂, branches along its 0 edge, the Boolean functionevaluates to FALSE, regardless of along which branch decision node 340,which represents variable x₃, proceeds. Thus, decision node 340 may bereplaced by the 0 terminal node. Similarly, paths 322 and 324 end at the1 terminal node. By examining the decision nodes on these two paths, itmay be determined that as long as decision node 350, which representsvariable x₂, branches along its 1 edge, the Boolean function evaluatesto TRUE, regardless of along which branches decision node 360, whichrepresents variable x₃, proceeds. Thus, decision node 360 may bereplaced by the 1 terminal node. As another example, consider decisionnodes 370 and 380, which both represent variable x₃. Decision nodes 370and 380 both have their 0 edge leading to the 0 terminal node and their1 edge leading to the 1 terminal node. Therefore, they are duplicates orisomorphic to each other. Thus, one of them may be removed from BDD 300.FIG. 3B illustrates an example BDD 390 representing the same Booleanfunction as repressed by BDD 300, but is more optimized than BDD 300because it uses fewer nodes to represent the same Boolean function as aresult of removing the redundant decision nodes and the isomorphicportions of BDD 300.

A BDD whose redundant decision nodes and isomorphic sub-graphs have beenremoved and whose decision nodes appear in the same order from the rootto the terminal nodes along all the paths in the BDD is referred to as areduced ordered binary decision diagram (ROBDD). The advantage of aROBDD is that it is canonical for a particular function and variableorder, which makes it useful in various types of practical applications,such as in functional equivalence checking and functional technologymapping.

A ROBDD has two important properties. First, the ROBDD is ordered. Thatis, there is a fixed order π{1, . . . , n}→{x₁, . . . , x_(n)} such thatfor any non-terminal node v, index(low(v))=π(k) with k>π⁻¹ (index(v))and index(high(v))=π(q) with q>π⁻¹ (index(v)) hold if low(v) and high(v)are also non-terminal nodes, where index(v) denotes the index of thevariable associated with node v, low(v) corresponds to the case wherethe variable associated with node v is assigned 0, and high(v)corresponds to the case where the variable associated with node v isassigned 1. Second, the ROBDD is reduced. That is, there exists nonon-terminal node vεV with low(v)=high(v) and there are no twonon-terminal nodes v and v′ such that the sub-BDDs rooted by v and v′are isomorphic. Note that a non-terminal node is a decision node. Forexample, in FIG. 3B, BDD 390 has three layers as it represents a Booleanfunction having three variables. Since BDD 390 is ordered, each layercontains the decision nodes that correspond to a particular variable.For example, layer 2 contains the decision nodes corresponding tovariable x₂ only, and does not contain any decision node correspondingto another variable (e.g., x₁ or x₃).

In additional to BDDs and ROBDDs, other examples of BDDs includepartitioned ordered binary decision diagrams (POBDDs), zero-suppresseddecision diagrams (ZDDs), nano binary decision diagrams (nanoDDs),zero-suppressed nano binary decision diagrams (nanoZDDs), or othersuitable binary decision diagrams. Although this disclosure discussesusing particular BDDs in particular, this disclosure contemplates usingany suitable type of BDD in any suitable applications.

BDDs have many practical applications, and the various algorithmsdisclosed in the present disclosure may be used with BDDs of anyapplications. As an example and not by way of limitation, in the fieldintegrated circuit (IC) design, an IC may be used to implement afunction, which may be represented by a BDD. Sometimes, a property thatan IC design needs to satisfy may be represented by a BDD, which maythen be used with in connection with formally verifying the design ofthe circuit. In the field of healthcare, BDDs may be used to representdata collected by medical sensors. A BDD, or more specifically, the datathat forms the BDD, may be stored in a computer-readable non-transitorystorage medium. When the variables of the BDD are processed using any ofthe algorithms described in this disclosure, the data is transformed asembodied by the computer-readable non-transitory storage medium.

In particular embodiments, any set of integers may be represented as aBoolean function, and the Boolean function may be represented by a BDD.Given a set of integers, particular embodiments may determine theminimum number of bits required to represent the largest integer in theset. This number of bits is the number of variables of the Booleanfunction. Then, for each integer in the set the Boolean functionevaluates to TRUE, and for any integer not in the set the Booleanfunction evaluates to FALSE.

In particular embodiments, a BDD may be used to represent one or moredata sets from one or more data streams. Each path in the BDD that leadsto the 1 terminal node indicates that the value (i.e., the data point)represented by all the decision nodes along that path belongs to thedata set. Similarly, each path in the BDD that leads to the 0 terminalnode indicates that the value represented by all the decision nodesalong that path is not included in the data set.

To represent a data set using a BDD, the minimum number of variablesneeded for the BDD equals the minimum number of bits needed to representthe largest value (i.e., data point) in the data set. As an example andnot by way of limitation, consider a data set comprising a set ofintegers, {3, 5, 6, 7}. The largest integer in the set is 7, whichrequires 3 bits. Thus, the Boolean function used to represent this setof integers requires three variables x₁, x₂, and x₃. The following tableillustrates the values of the three variables and the Boolean functionas they are used to represent {3, 5, 6, 7}:

Binary Value Decimal Value x₁, x₂, x₃ f(x₁, x₂, x₃) 0 0 0 0 0 1 0 0 1 02 0 1 0 0 3 0 1 1 1 4 1 0 0 0 5 1 0 1 1 6 1 1 0 1 7 1 1 1 1

The function ƒ(x₁, x₂, x₃) may be represented by BDD 300 illustrated inFIG. 3A or BDD 390 illustrated in FIG. 3B.

In particular embodiments, one or more components of sensor network 100may store one or more BDDs in a BDD library. The BDD library may includeany suitable information about a BDD, such as, for example, nodestructure, each binary variable, indices to the nodes that correspond tothe two possible evaluations of the variables, complementation of theindices, or other suitable information about the BDD. In particularembodiments, the BDD library may store the information compactly. As anexample and not by way of limitation, a BDD library may maintain theindices and variable identifiers as a function of the size of the BDD.The BDD may have at most k nodes throughout some or all manipulationsperformed by BDD library. Each node of the BDD may be labeled with oneof at most v variable identifiers. The indices to nodes thereforerequire at most ┌ log(v)┐ bits to index any variable. The node thereforerequires only 2·┌ log(k)┐+┌ log(v)┐ bits. In addition, two bits may bereserved, one bit used to identify complemented edges (allowing therepresentation of a function as well as its negation by a single node)and another bit used as a general mark bit used during garbagecollection. Values for v and k may be determined in any suitable manner.For example, a user may specify v and a default k value may be usedinitially. When the address space allowed by the default k value isexhausted, the k value may be increased and the node table may berebuilt. In another example, maximum values for v and k may be assumed.

In particular embodiments, one or more components of sensor network 100may store sensor data as one or more BDDs. One or more sensors 112 insensor array 110 may take a plurality of samples (i.e., receive aplurality of stimuli) and produce a data set S based on the samples. Inparticular embodiments, each sample comprises a tuple of one or moresensor values. Each sensor value records one or more stimuli received byone or more sensors. Data set S may be generated in any suitable manner.In particular embodiments, time may be quantized according to thesampling frequency of the sensor 112 or for desired accuracy. For eachtime t, set S of sensor values is obtained to yield S={(t_(i), q_(i) ¹,. . . , q_(i) ^(k))}, where q_(i) ^(j) is the quantized input fromsensor j at time instance i. Each sample is represented as a minterm. Inparticular embodiments, one or more variables may be allocated to eachdata value of a sample. As an example and not by way of limitation, Ntvariables may be allocated for time, Ns1 variables may be allocated fora first sensor, and Ns2 variables may be allocated for a second sensor.Therefore, a sample would correspond to a minterm of the form t₁ . . .t_(Nt)·s₁ ¹ . . . s_(Ns1) ¹·s₁ ² . . . s_(Ns2) ². For example, if Nt=16,Ns1=8, and Ns2=8, then a sample would correspond to a minterm of theform t₁ . . . t₁₆·s₁ ¹ . . . s₈ ¹·s₁ ² . . . s₈ ². Each sensor samplemay be expressed as a binary number using the allocated variables. Inthe example, a subset of S may be {(1,70,3), (2,70,3), (3,70,4)}. Therelated minterms are:

0000000000000001·01000110·00000011,

0000000000000010·01000110·00000011,

0000000000000011·01000110·00000100.

In particular embodiments, a characteristic function ƒ^(s) may begenerated from a set of minterms. The characteristic function ƒ^(s) maybe generated in any suitable manner. As an example and not by way oflimitation, a logical operation may be applied to the minterms togenerate characteristic function ƒ^(S). This disclosure contemplates anygenerating characteristic functions using suitable logical operations.As an example and not by way of limitation, a logical operation mayinclude AND, OR, XOR, NOT, or a combination of two or more of these.Applying a logical OR operation to a number of operands yields thelogical OR of the operands. The corresponding characteristic functionƒ^(s)({right arrow over (t)};{right arrow over (s)}¹;{right arrow over(s)}²) is the logical OR of all minterms. A characteristic functionƒ^(s) may be updated to include additional data sets in any suitablemanner. As an example and not by way of limitation, a new data set maybe represented as a new set of minterms, and a logical OR operation maybe applied to the characteristic function ƒ^(s) and the new set ofminterms to yield an updated characteristic function ƒ^(S).

A characteristic function ƒ^(s) may be reported in any suitable manner.As an example and not by way of limitation, display system 190 mayfacilitate display of characteristic function ƒ^(s) at a suitable I/Odevice.

Analysis

Analysis system 180 may monitor, store, and analyze one or more datastreams from one or more sensors 112 in sensor array 110. A data streamfrom a sensor 112 may be transmitted to analysis system 180 over anysuitable medium. Analysis system 180 may transmit one or more analysisoutputs based on the one or more data streams to one or more othercomponents of sensor network 100, such as, for example, sensors 112,other analysis systems 180, or display systems 190. Analysis system 180may be any suitable computing device, such as, for example, computersystem 1700.

In particular embodiments, analysis system 180 may comprise one or morelocal analysis systems 120 or one or more remote analysis systems 150.Where analysis system 180 comprises multiple subsystems (e.g., localanalysis system 120 and remote analysis system 150), processing andanalysis of the data streams may occur in series or in parallel. As anexample and not by way of limitation, analysis system 180 may receiveidentical data streams from a sensor 112 at both local analysis system120 and remote analysis system 150. As another example and not by way oflimitation, analysis system 180 may receive a data stream at localanalysis system 120, which may process the data stream and then transmita modified data stream/analysis output to remote analysis system 150.

In particular embodiments, analysis system 180 may access and analyzeone or more data sets from a data stream. Analysis system 180 mayanalyze a data stream in real-time as it is received from sensor array110, or it may store the data stream after it is received from sensorarray 110 for subsequently processing the data stream. Analysis system180 may use any suitable process, calculation, or technique to analyze adata stream. As an example and not by way of limitation, analysis system180 may perform a variety of processes and calculations, includingranging, inspecting, cleaning, filtering, transforming, modeling,normalizing, averaging, annotating, correlating, or contextualizingdata. As another example and not by way of limitation, analysis system180 may use a variety of data analysis techniques, including datamining, data fusion, distributed database processing, or artificialintelligence. These techniques may be applied to analyze various datastreams and to generate correlations and conclusions based on the data.Analysis system 180 may analyze a plurality of data streams to determineif the data streams are related. A relationship between data streams mayinclude, for example, correlations, causal relationships, dependentrelationships, reciprocal relationships, data equivalence, anothersuitable relationship, or two or more such relationship. In particularembodiments, analysis system 180 may access or generate one or more BDDsrepresenting one or more data streams and perform a variety of processesand calculations on the BDDs. Although this disclosure describesanalysis system 180 performing particular analytical processes usingparticular techniques, this disclosure contemplates analysis system 180performing any suitable analytical processes using any suitabletechniques.

In particular embodiments, analysis system 180 may generate models basedon one or more data streams. A model is a means for describing a systemor object. As an example and not by way of limitation, a model may be adata set, function, algorithm, differential equation, chart, table,decision tree, binary decision diagram, simulation, another suitablemodel, or two or more such models. A model may describe a variety ofsystems or objects, including one or more aspects of one or morepersons' physiology, psychology, behavior, or environment. Although thisdisclosure describes particular components generating particular models,this disclosure contemplates any suitable components generating anysuitable models. Moreover, although this disclosure describes generatingparticular models using particular techniques, this disclosurecontemplates generating any suitable models using any suitabletechniques.

Analysis system 180 may generate models that are empirical, theoretical,linear, nonlinear, deterministic, probabilistic, static, dynamic,heterogeneous, or homogenous. Analysis system 180 may generate modelsthat fit one or more data points using a variety of techniques,including, for example, curve fitting, model training, interpolation,extrapolation, statistical modeling, nonparametric statistics,differential equations, etc.

Analysis system 180 may generate models of various types, includingbaseline models, statistical models, predictive models, etc. A baselinemodel is a model that serves as a basis for comparison, and is typicallygenerated using controlled data (i.e., baseline data) over a specifiedperiod (i.e., a control period). The control period may be any suitableperiod. As an example and not by way of limitation, a baseline model ofa subject's blood pressure may simply be the subject's average bloodpressure calculated from a series of blood-pressure measurements takenover the course of a week by a blood-pressure monitor. A predictivemodel is a mathematical function (or set of functions) that describe thebehavior of a system or object in terms of one or more independentvariables. As an example and not by way of limitation, a predictivemodel that may be used to calculate a physiological state based on oneor more actual sensor measurements. A type of predictive model is astatistical model, which is a mathematical function (or set offunctions) that describe the behavior of an object of study in terms ofrandom variables and their associated probability distributions. One ofthe most basic statistical models is the simple linear regression model,which assumes a linear relationship between two measured variables. Asan example and not by way of limitation, analysis system 180 may comparedata from a pulse oximeter and a barometer and identify a linearcorrelation between a subject's blood-oxygen level and the barometricpressure at the subject's location. In particular embodiments, apredictive model may be used as a baseline model, wherein the predictivemodel was generated using controlled data over a specified period.

In particular embodiments, analysis system 180 may generate a model bynormalizing or averaging one or more data streams. As an example and notby way of limitation, a model of a data stream from a single sensor 112could simply be the average sensor measurement made by the sensor 112over some initialization period. As another example and not by way oflimitation, a model could be a single sensor measurement made during acontrol period.

In particular embodiments, analysis system 180 may generate a model byfitting one or more data sets to a mathematical function. As an exampleand not by way of limitation, a model could be an algorithm based onsensor measurements made by one or more sensors over some controlperiod. The model may include a variety of variables, including datafrom one or more data streams and one or more fixed variables. Thefollowing is an example algorithm that analysis system 180 couldgenerate to model a system or object:

f _(m) =f(D _(sensor) ¹ , . . . ,D _(sensor) ^(N) ,Y ¹ , . . . ,Y ^(M))

where:

-   -   f_(m) is the model,    -   (D_(sensor) ¹, . . . , D_(sensor) ^(N)) are data streams 1        through N, and    -   (Y¹, . . . , Y^(M)) are fixed variables 1 through M.

In particular embodiments, the model may be used to predict hypotheticalsensor measurements in theoretical or experimental systems. Inparticular embodiments, the model may be used to determine or categorizea subject's physiological or psychological state. As an example and notby way of limitation, the model may determine a subject's risk for acertain disease state with an abstract or statistical result. The modelcould simply identify the subject as being at “high risk” of developinga disease, or identify the subject as being 80% likely to develop thedisease. As another example and not by way of limitation, the model maydetermine a subject's severity or grade of a disease state.

In particular embodiments, one or more sensors 112 in sensor array 110may continuously transmit data regarding a subject's health to analysissystem 180, which may monitor and automatically detect changes in thesubject's health state. As used herein, “health state” refers to aperson's physiological and psychological state, including the person'sstate with respect to pathologies and diseases. By using an integratedsensor array 110 to monitor physiological, psychological, behavioral,and environmental data, analysis system 180 may identify pathologies,disease states, sensitivities, and other health-related states withgreater accuracy than is possible with any individual sensor 112.

In particular embodiments, one or more sensors 112 in sensor array 110may measure one or more biomarkers. A biomarker is a characteristic thatcan be measured and evaluated as an indicator of biological processes,pathogenic processes, or pharmacologic responses. As an example and notby way of limitation, in a pharmacogenomic context, a biomarker would bea specific genetic variation that correlates with drug response. Asanother example and not by way of limitation, in a neurochemicalcontext, a biomarker would be a person's subjective stress level thatcorrelates with the person's plasma glucocorticoid level. As yet anotherexample and not by way of limitation, in a neuropsychological context, abiomarker would be a person's serotonin uptake rate that correlates withthe person's depression level. As yet another example and not by way oflimitation, in a biochemical context, a biomarker would be a person'sLDL cholesterol level that correlates with the person's risk of heartdisease, such as heart attack. A biomarker is effectively a surrogatefor measuring another physiological or psychological characteristic. Abiomarker may include any type of stimulus, including physiological,psychological, behavioral, or environmental stimulus.

In particular embodiments, analysis system 180 may identify pathologies,disease states, and other health states of a subject. Certainphysiological, psychological, behavioral, or environmental data maycorrelate with certain pathologies, disease states, and other healthstates. As an example and not by way of limitation, analysis system 180could determine whether a subject has hypertension by monitoring a bloodpressure data stream for a three week period and identifying substantialperiods where the subject's blood pressure is at least 140/90 mmHg,wherein these substantial periods of elevated blood pressure constitutehypertension. The accuracy of identification may generally be increasedas the number of data streams is increased. Analysis system 180 maycontextualize and correlate data from multiple data streams to eliminateconfounders from its data analysis and reduce the likelihood ofgenerating false-positive and false-negative disease-state diagnoses. Asan example and not by way of limitation, the hypertension diagnosissystem described above may generate a false-positive diagnosis ofhypertension if the subject engages in lengthy periods of physicalactivity, which naturally raise the subject's blood pressure. Therefore,if analysis system 180 also monitored a heart-rate data stream of thesubject, it could eliminate blood pressure data sets that correlate withtime periods of high heart-rate, thereby reducing the likelihood ofgenerating an incorrect hypertension diagnosis.

In particular embodiments, analysis system 180 may analyzephysiological, psychological, behavioral and environmental data steamsto identify correlations between certain data sets and a subject'shealth state. As an example and not by way of limitation, analysissystem 180 may be able to correlate a behavioral data set indicating thesubject had a fight with a physiological data set indicating the subjecthad an elevated heart-rate to identify the fight as the cause of theelevated heart-rate. As another example and not by way of limitation,analysis system 180 may be able to correlate a physiological data setindicating the subject had an elevated skin temperature with abehavioral data set indicating the subject was engaged in physicalactivity to identify the physical activity as the cause of the elevatedskin temperature. As yet another example and not by way of limitation,analysis system 180 may be able to correlate a psychological data setindicating the subject is depressed with an environmental data setindicating that the subject's stock portfolio substantially declinedjust prior to the onset of the subject's depression to identify thestock decline as the cause of the subject's depression. Analysis system180 may use a variety of methods to identify correlations and generatecausality hypotheses.

In particular embodiments, analysis system 180 may generate a model of asubject's health state. As an example and not by way of limitation,analysis system 180 may generate a baseline model of the subject'sphysiological or psychological state by analyzing one or more datastreams during a control period. Once the baseline model is established,analysis system 180 could then continuously monitor the subject andidentify deviations, variability, or changes in the data streams ascompared to the baseline model. As another example and not by way oflimitation, analysis system 180 may generate a predictive model of thesubject's physiological or psychological state by analyzing one or moredata streams and generating one or more algorithms that fit the sensormeasurements. Once the predictive model is established, analysis system180 could then be used to predict future health states, anticipated orhypothetical sensor readings, and other aspects of a subject'sphysiology or psychology. Analysis system 180 may also update and refinethe predictive model based on new data generated by sensor array 110.

In particular embodiments, analysis system 180 may monitor disease-stateprogression and other health state changes over time. As an example andnot by way of limitation, analysis system 180 could continuously monitora subject's blood pressure over time to determine whether the subject'shypertension is improving. Such monitoring may be used to identifytrends and to generate alerts or predictions regarding possible healthstates. Similarly, analysis system 180 may also monitor data streamscontaining treatment or therapy information to determine whether thetreatment or therapy is efficacious. As an example and not by way oflimitation, analysis system 180 could monitor a subject's blood pressureover time to determine whether an ACE inhibitor treatment is affectingthe subject's hypertension.

In particular embodiments, analysis system 180 may monitor and analyzevarious data streams from a group of people to identify novelpre-disease states or risk states. As an example and not by way oflimitation, one or more sensor arrays 110 could monitor a plurality ofsubjects. As multiple subjects develop certain diseases, analysis system180 could analyze data sets from these subjects prior their developmentof the disease. The analysis of these data sets could allow analysissystem 180 to identify certain health states that correlate with somelevel of risk for developing the disease.

Combining/Partitioning Medical Binary Decision Diagrams for AnalysisOptimization

In particular embodiments, sensor network 100 may construct one or moreBDDs for analysis optimization from one or more other BDDs. Analysisoptimization refers to increasing the speed or efficiency of ananalytical process. As an example and not by way of limitation, sensornetwork 100 may partition a BDD into a plurality of sub-BDDs based onease-of analysis. As another example and not by way of limitation,sensor network 100 may combine one or more portions of a plurality ofBDDs into a new BDD based on ease-of-analysis. Although this disclosuredescribes particular components performing particular processes toconstruct one or more BDDs for analysis optimization from one or moreother BDDs, this disclosure contemplates using any suitable componentsto construct one or more BDDs for analysis optimization from one or moreother BDDs.

In particular embodiments, analysis system 180 may access one or moreBDDs representing one or more data streams from a plurality of sensors112. Each data stream may comprise a plurality of components. FIG. 4illustrates an example data stream with a plurality of components. As anexample and not by way of limitation, analysis system 180 may access aBDD representing the data stream illustrated in FIG. 4, which is aschematic of a single interval of a typical electrocardiograph (ECG)wave measuring the microvoltages in a heart muscle over time. AlthoughFIG. 4 illustrates a single ECG wave in a data stream, this disclosurecontemplates any suitable number of ECG waves in the data stream. Thecomponents of an ECG wave may include a PR interval, a QT interval, a PRsegment, a QRS complex, and a ST segment. A component of a data streammay overlap in whole or in part with another component of the datastream. As an example and not by way of limitation, the ST segmentoverlaps in whole with the QT interval. Although this disclosuredescribes and FIG. 4 illustrates a particular data stream withparticular components, this disclosure contemplates any suitable datastream with any suitable components. A BDD representing a data streammay comprise a plurality of portions, wherein each portion representsone component of the data stream. A portion of a BDD may include a pathor set of paths in the BDD. As an example and not by way of limitation,the ECG wave illustrated in FIG. 4 may be represented by a BDD, such asBDD_(E1), and each component of the ECG wave may be represented by aportion of BDD_(E1). Each portion of a BDD may be represented by asub-BDD that represents the component of the data stream represented bythe portion. As an example and not by way of limitation, the PRinterval, QT interval, PR segment, QRS complex, and ST segment may berepresented by BDDs BDD_(PR1), BDD_(QT1), BDD_(PR1), BDD_(QRS1), andBDD_(ST1), respectively, which are sub-BDDs of BDD_(E1). Although thisdisclosure describes accessing particular BDDs representing particulardata streams, this disclosure contemplates accessing any suitable BDDsrepresenting any suitable data streams. Moreover, although thisdisclosure describes particular components accessing BDDs, thisdisclosure contemplates any suitable components accessing BDDs.

In particular embodiments, analysis system 180 may identify thecomponents in a data stream. The components of a data stream may beidentified in any suitable manner. In particular embodiments, analysissystem 180 may identify components in a data stream based on thestructural characteristics of the data stream. A structuralcharacteristic of a data stream may be a structural characteristics of awaveform of a signal outputted by a sensor 112, a periodicity of awaveform of a signal outputted by a sensor 112, an identifier embeddedin the data stream defining a component, another suitable structuralcharacteristics, or two or more such structural characteristics. As anexample and not by way of limitation, a component of an ECG wave may beidentified based on structural characteristics of the waveform outputtedby an electrocardiograph. Referring to FIG. 4, the PR segment may beidentified as the component of the heart wave between the P wave and theQRS complex. The structure of P wave and the QRS complex can be definedby the shape of the components (i.e., the microvoltage versus timecurve). As another example and not by way of limitation, a component ofan ECG wave may be identified based on the periodicity of the waveformoutputted by an electrocardiograph. Referring to FIG. 4, the periodicityof the waveform can be defined by the interval between an R wave and thenext R wave (the RR interval), which is the inverse of the heart rateand occurs regularly. As yet another example and not by way oflimitation, a component of an ECG wave may be identified based on anidentifier embedded in the data stream defining the component. Referringto FIG. 4, an electrocardiograph may embed an identifier in thewaveform, such as, for example, a peak after the T wave, to identify theend of the heart wave. In particular embodiments, analysis system 180may identify components in a data stream based on the functionalcharacteristics of the data stream. A functional characteristic of adata stream may be a rate of change of a waveform of a signal outputtedby a sensor 112, minimum and/or maximum values of a waveform of a signaloutputted by a sensor 112, another suitable functional characteristic,or two or more such functional characteristics. In particularembodiments, analysis system 180 may identify components in a datastream based on predefined component definitions provided by a user oranother suitable source. As an example and not by way of limitation, acomponent of an ECG wave may be specified by a user. Referring to FIG.4, a user may define a “PT interval” that consists of the PR segment,the QRS complex, and the ST segment. Although this disclosure describesidentifying particular components in particular data streams, thisdisclosure contemplates identifying any suitable components in anysuitable data streams. Moreover, although this disclosure describesparticular processes for identifying components in a data stream, thisdisclosure contemplates any suitable processes for identifyingcomponents in a data stream.

In particular embodiments, analysis system 180 may select one or moreportions from a plurality of portions in one or more BDDs based onease-of-analysis. Ease-of-analysis refers to modifying one or more datasets to increase the speed or efficiency of an analytical process thatreferences the data sets. Data sets may be modified for ease-of-analysisby combining, partitioning, compressing, restructuring, consolidating,adjusting, reorganizing, rewriting, annotating, or otherwise suitablymodifying the data sets. As an example and not by way of limitation, anease-of-analysis decomposition may refer to decomposing a BDDrepresenting the ECG wave of FIG. 4 into BDDs representing the majorcomponents of the ECG signal, such as the PR interval, the QRS complex,and the QT interval. In particular embodiments, ease-of-analysis may bewith respect to a particular analytic process. Analysis system 180 mayreceive information describing a particular analytical process and thenidentify one or more components from one or more data streams needed forthe particular analytical process. Analysis system 180 may then selectthe portions of a BDD that represent the identified components. As anexample and not by way of limitation, analysis system 180 may receiveinformation describing an analytical process to determine the heart rateof a person. Referring to FIG. 4, the interval between an R wave and thenext R wave (the RR interval) is the inverse of the heart rate. Analysissystem 180 may identify the QRS complexes as the component of datastream needed to determine the heart rate of the person, and additionalcomponents of the data stream are not needed. Analysis system 180 maythen select the portions of the BDD that represent the QRS complexes.

In particular embodiments, ease-of-analysis may be with respect to thecompression rate achieved by constructing a sub-BDD from the selectedcomponent. A higher compression rate may lead to faster manipulation ofa dataset and therefore easier analysis, however such a correlation isnot always present or necessary. As an example and not by way oflimitation, analysis system 180 may be able to achieve a highercompression rate by constructing sub-BDDs from various components of anECG wave compared to storing the ECG wave as a single BDD. Referring toFIG. 4, the ECG wave illustrated may be stored as BDD_(E1). BDD_(E1) maybe partitioned into sub-BDDs, such as BDD_(QRS1) for storing QRS complexdata and BDD_(E2) for storing the remainder of the ECG wave. BecauseBDD_(QRS1) only stores the portion of the data stream containing QRScomplexes, it may have a relatively high compression rate. Furthermore,the sum of the sizes of BDD_(QRS1) and BDD_(E2) may be less than thesize of BDD_(E1). Although this disclosure describes selectingparticular portions of particular BDDs, this disclosure contemplatesselecting any suitable portions of any suitable BDDs. Moreover, althoughthis disclosure describes ease-of-analysis with respect to particularfactors, this disclosure contemplates ease-of-analysis with respect toany suitable factors.

In particular embodiments, analysis system 180 may construct a pluralityof sub-BDDs by partitioning a first BDD. The sub-BDDs may comprise afirst sub-BDD representing the portions selected based onease-of-analysis, and one or more second sub-BDDs representing thenon-selected portions. The sub-BDDs may be constructed in any suitablemanner. A BDD may be partitioned into a plurality of sub-BDDs accordingto existing BDD partition rules. As an example and not by way oflimitation, a BDD representing Boolean function ƒ(x₁, . . . , x_(n)) maybe partitioned into two or more sub-BDDs representing Boolean functionsƒ₁(x₁, . . . , x_(n)) to ƒ_(m) (x₁, . . . , x_(n)). Each of the Booleanfunctions may be considered a partition of the original Boolean functionƒ. If each of the Boolean functions ƒ₁ to ƒ_(m) is represented by a BDD,then the BDD that represents the original Boolean function ƒ may beobtained by logically ORing all the BDDs that represent the partitionsof f (i.e., f₁ to f_(m)). As another example and not by way oflimitation, a BDD representing the ECG wave illustrated in FIG. 4,BDD_(E1), may be partitioned into two or more sub-BDDs representingvarious components of the ECG wave, such as BDD_(QRS1) representing theQRS complex and BDD_(E2) representing the remainder of the ECG wave. Inparticular embodiments, analysis system 180 may then perform aparticular analytical process with one or more of the sub-BDDs. Inparticular embodiments, analysis system 180 may then store the firstsub-BDD representing the portions selected based on ease-of-analysis,and delete one or more of the second sub-BDDs representing thenon-selected portions. Although this disclosure describes constructing aplurality of sub-BDDs by partitioning a first BDD using particularcomponents and particular processes, this disclosure contemplatesconstructing a plurality of sub-BDDs by partitioning a first BDD usingany suitable components and any suitable processes.

In particular embodiments, analysis system 180 may construct a secondBDD by combining a plurality of portions from a plurality of first BDDs.The plurality of portions may comprise the portions selected based onease-of-analysis. As an example and not by way of limitation, portionsmay be selected based on whether the combined BDD requires less space. Asecond BDD may be constructed from a plurality of portions of first BDDsin any suitable manner. As an example and not by way of limitation, aplurality of first BDDs representing Boolean functions ƒ₁(x₁, . . . ,x_(n)) to ƒ_(m)(x₁, . . . , x_(n)) may be combined into a second BDDrepresenting Boolean function F(x₁, . . . , x_(n)). Each of the Booleanfunctions ƒ₁(x₁, . . . , x_(n)) to ƒ_(m)(x₁, . . . , x_(n)) may beconsidered a partition of the Boolean functions represented by theplurality of first BDDs. If each of the Boolean functions ƒ₁ to ƒ_(m) isrepresented by a BDD, then the second BDD that represents the Booleanfunction F may be obtained by logically ORing all the BDDs thatrepresent f₁ to f_(m). As another example and not by way of limitation,a plurality of portions from a plurality of first BDDs representing aplurality of ECG waves, like the wave illustrated in FIG. 4, may becombined into a second BDD. The portion of each first BDD representingthe QRS complex may be combined into a second BDD representing the QRScomplex from each first BDD. In particular embodiments, analysis system180 may then perform a particular analytical process with the secondBDD. In particular embodiments, analysis system 180 may then store thesecond BDD representing the portions of the first BDDs selected based onease-of-analysis, and delete one or more of the first BDDs. Althoughthis disclosure describes constructing a second BDD by combining aplurality of portions from a plurality of first BDDs using particularcomponents and particular processes, this disclosure contemplatesconstructing a second BDD by combining a plurality of portions from aplurality of first BDDs using any suitable components and any suitableprocesses.

In particular embodiments, analysis system 180 may optimize the size ofa BDD before combining or partitioning the BDD. As an example and not byway of limitation, analysis system 180 may optimize the size of the BDDusing variable reordering.

FIG. 5 illustrates an example method for combining medical binarydecision diagrams for analysis optimization. The method begins at step510, where analysis system 180 accesses a plurality of first BDDsrepresenting a plurality of data streams from a plurality of sensors112. The plurality of data streams comprise a plurality of componentsand the first BDDs comprise a plurality of portions, wherein eachportion represents one component. At step 520, analysis system 180selects one or more portions from the plurality of portions in the firstBDDs based on ease-of-analysis. At step 530, analysis system 180constructs a second BDD by performing an OR operation between theselected portions of the first BDDs. Although this disclosure describesand illustrates particular steps of the method of FIG. 5 as occurring ina particular order, this disclosure contemplates any suitable steps ofthe method of FIG. 5 occurring in any suitable order. Moreover, althoughthis disclosure describes and illustrates particular components carryingout particular steps of the method of FIG. 5, this disclosurecontemplates any suitable combination of any suitable componentscarrying out any suitable steps of the method of FIG. 5.

FIG. 6 illustrates an example method for partitioning medical binarydecision diagrams for analysis optimization. The method begins at step610, where analysis system 180 accesses a first BDD representing one ormore data streams from one or more sensors 112, wherein the one or moredata streams comprise a plurality of components and the first BDDcomprises a plurality of portions, wherein each portion represents onecomponent. At step 620, analysis system 180 selects one or more portionsfrom the plurality of portions in the first BDD based onease-of-analysis. At step 630, analysis system 180 constructs aplurality of sub-BDDs by partitioning the first BDD, wherein theplurality of sub-BDDs comprises a first sub-BDD representing theselected portions, and one or more second sub-BDDs representing one ormore of the non-selected portions. Although this disclosure describesand illustrates particular steps of the method of FIG. 6 as occurring ina particular order, this disclosure contemplates any suitable steps ofthe method of FIG. 6 occurring in any suitable order. Moreover, althoughthis disclosure describes and illustrates particular components carryingout particular steps of the method of FIG. 6, this disclosurecontemplates any suitable combination of any suitable componentscarrying out any suitable steps of the method of FIG. 6.

Combining/Partitioning Medical Binary Decision Diagrams for SizeOptimization

In particular embodiments, sensor network 100 may construct one or moreBDDs for size optimization from one or more other BDDs. Sizeoptimization refers to decreasing the size or increasing the compressionratio of data for storing or processing. As an example and not by way oflimitation, sensor network 100 may combine a plurality of first BDDsinto one or more second BDDs based on size optimization. As anotherexample and not by way of limitation, sensor network 100 may partition aBDD into a plurality of sub-BDDs based on size optimization. Althoughthis disclosure describes particular components performing particularprocesses to construct one or more BDDs for size optimization from oneor more other BDDs, this disclosure contemplates using any suitablecomponents to construct one or more BDDs for size optimization from oneor more other BDDs.

In particular embodiments, analysis system 180 may access one or moreBDDs representing one or more data streams from a plurality of sensors112. Each data stream may comprise a plurality of components. A BDDrepresenting a data stream may comprise a plurality of portions, whereineach portion represents one component of the data stream. A portion of aBDD may include a path or set of paths in the BDD. Each portion of a BDDmay be represented by a sub-BDD that represents the component of thedata stream represented by the portion. As an example and not by way oflimitation, analysis system 180 may access BDD_(E1) representing thedata stream illustrated in FIG. 4.

In particular embodiments, analysis system 180 may construct a secondBDD by combining a plurality of first BDDs. A second BDD may beconstructed from the plurality of first BDDs by any suitable process. Asan example and not by way of limitation, a plurality of first BDDsrepresenting Boolean functions ƒ₁(x₁, . . . , x_(n)) to ƒ_(m)(x₁, . . ., x_(n)) may be combined into a second BDD representing Boolean functionF(x₁, . . . , x_(n)). If each of the Boolean functions ƒ₁ to ƒ_(m) isrepresented by a first BDD, then the second BDD that represents theBoolean function F may be obtained by logically ORing all the first BDDsthat represent f₁ to f_(m). As another example and not by way oflimitation, a plurality of first BDDs representing a plurality of ECGwaves, like the wave illustrated in FIG. 4, may be combined into secondBDD representing the plurality of ECG waves. Although this disclosuredescribes constructing a second BDD by combining a plurality of firstBDDs using particular components and particular processes, thisdisclosure contemplates constructing a second BDD by combining aplurality of first BDDs using any suitable components and any suitableprocesses.

In particular embodiments, analysis system 180 may select one or moreportions from a plurality of portions in one or more first BDDs. As anexample and not by way of limitation, analysis system 180 may select oneor more portions of a BDD representing Boolean function ƒ(x₁, . . . ,x_(n)). As another example and not by way of limitation, analysis system180 may select the portions of BDD_(E1) that represent the QRS complexesillustrated in FIG. 4. In particular embodiments, analysis system 180may then construct a second BDD representing the selected portions and athird BDD representing the non-selected portions. The second and thirdBDDs may be constructed in any suitable manner, such as, for example, bypartitioning the first BDD into the second and third BDDs according toexisting BDD partition rules. As an example and not by way oflimitation, a first BDD representing Boolean function ƒ(x₁, . . . ,x_(n)) may be partitioned into one or more second BDDs representingBoolean functions ƒ₁ ^(s)(x₁, . . . , x_(n)) to ƒ_(m) ^(s)(x₁, . . . ,x_(n)), which represent the selected portions of the first BDD, and oneor more third BDDs representing Boolean functions ƒ₁ ^(ns)(x₁, . . . ,x_(n)) to ƒ_(p) ^(ns)(x₁, . . . , x_(n)), which represent thenon-selected portions of the first BDD. Each of the Boolean functions tomay be considered a partition of the original Boolean function ƒ. Ifeach of the Boolean functions ƒ₁ ^(s) to ƒ_(m) ^(s) and ƒ₁ ^(ns) toƒ_(p) ^(ns) is represented by a BDD, then the BDD that represents theoriginal Boolean function ƒ may be obtained by logically ORing all theBDDs that represent the partitions of f (i.e., f₁ ^(s) to f_(m) ^(s) andf₁ ^(ns) to f_(p) ^(ns)). As another example and not by way oflimitation, a BDD representing the ECG wave illustrated in FIG. 4,BDD_(E1), may be partitioned into two or more sub-BDDs representingvarious components of the ECG wave. If the selected portion is theportion representing the QRS complex, then analysis system 180 maypartition BDD_(E1) into such as BDD_(QRS1) representing the QRS complexand BDD_(E2) representing the unselected portions of BDD_(E1), whereinBDD_(E2) represents the remainder of the ECG wave. Although thisdisclosure describes constructing a second BDD representing the selectedportions and a third BDD representing the non-selected portions usingparticular components and particular processes, this disclosurecontemplates constructing a second BDD representing the selectedportions and a third BDD representing the non-selected portions usingany suitable components and any suitable processes.

In particular embodiments, analysis system 180 may determine the size ofone or more BDDs. The size of a BDD may be based on the function the BDDrepresents and the ordering of variables in the BDD. The size of a BDDmay be directly obtained from the number of nodes in the BDD. As anexample and not by way of limitation, a BDD may have a size expressed asa number of bits that indicate how much storage is associated with theBDD. In particular embodiments, analysis system 180 may optimize thesize of one or more BDDs before determining the size of the BDDs. As anexample and not by way of limitation, analysis system 180 may optimizethe size of the BDD using variable reordering. Although this disclosuredescribes particular processes for determining the size of a BDD, thisdisclosure contemplates any suitable processes for determining the sizeof a BDD.

In particular embodiments, analysis system 180 may compare the sizes ofthe one or more original BDDs and the one or more BDDs that wereconstructed by combining or partitioning the original BDDs. The sizes ofthe BDDs may be compared in any suitable manner. As an example and notby way of limitation, analysis system 180 may determine the number ofbits needed to store a BDD on a particular data store. In particularembodiments, analysis system 180 may store the BDDs with smaller sizesand delete the BDDs with larger sizes after comparing the sizes of theBDDs. A BDD may be stored on any suitable data store. As an example andnot by way of limitation, where a second BDD was constructed bycombining a plurality of first BDDs, if the size of the second BDD isless than the sum of the sizes of the first BDDs, then analysis system180 may store the second BDD and delete the first BDDs; else, analysissystem 180 may store the first BDDs and delete the second BDD. Asanother example and not by way of limitation, where a first BDD ispartitioned into a second and third BDDs, if the size of the first BDDis less than the sum of the sizes of the second and third BDDs, thenanalysis system 180 may store the first BDD and delete the second andthird BDDs; else, analysis system 180 may store the second and thirdBDDs and delete the first BDD. Although this disclosure describescomparing the sizes of particular BDDs, this disclosure contemplatescomparing the sizes of any suitable BDDs. Moreover, although thisdisclosure describes storing and deleting BDDs based on particular sizecomparisons, this disclosure contemplates storing and deleting BDDsbased on any suitable size comparisons.

Although this disclosure describes combining a particular number of BDDsfor size optimization, this disclosure contemplates combining anysuitable number of BDDs for size optimization. As an example and not byway of limitation, analysis system 180 may access a first BDDrepresenting a first data stream from a first sensor 112, a second BDDrepresenting a second data stream from a second sensor 112, and a thirdBDD representing a third data stream from a third sensor 112. Analysissystem 180 may then construct a fourth BDD by performing an OR operationbetween the first and second BDDs, construct a fifth BDD by performingan OR operation between the first and third BDDs, construct a sixth BDDby performing an OR operation between the second and third BDDs, andconstruct a seventh BDD by performing an OR operation between the firstBDD, the second BDD, and the third BDD. Analysis system 180 may thendetermine a first size of the first BDD, a second size of the secondBDD, and a third size of the third BDD, a fourth size of the fourth BDD,a fifth size of the fifth BDD, a sixth size of the sixth BDD, a seventhsize of the seventh BDD, a sum of the sizes of the first and sixth BDDs,a sum of the sizes of the second and fifth BDDs, a sum of the sizes ofthe third and fourth BDDs, and a sum of the sizes of the first, second,and third BDDs. Analysis system 180 may then select the smallest sizefrom the group consisting of: the seventh size of the seventh BDD; thesum of the sizes of the first and sixth BDDs; the sum of the sizes ofthe second and fifth BDDs; the sum of the sizes of the third and fourthBDDs; and the sum of the sizes of the first, second, and third BDDs.Analysis system 180 may then store the BDDs corresponding to theselected group and delete the remaining BDDs.

Although this disclosure describes partitioning a BDD into a particularnumber of BDDs for size optimization, this disclosure contemplatespartitioning a BDD into any suitable number of BDDs for sizeoptimization. As an example and not by way of limitation, analysissystem 180 may access a first BDD representing one or more data streamsfrom one or more sensors 112. The data streams may comprise a pluralityof components. The first BDD may comprise a plurality of portions,wherein each portion represents one or more components of one or moredata streams. Analysis system 180 may then select one or more firstportions from the plurality of portions in the first BDD and select oneor more second portions from the plurality of portions in the first BDD.Analysis system 180 may then construct a second BDD representing thefirst selected portions, construct a third BDD representing the secondselected portions, construct a fourth BDD representing the non-selectedportions, construct a fifth BDD representing a combination of the firstand second selected portions, construct a sixth BDD representing acombination of the second selected portions and the non-selectedportions, and construct a seventh BDD representing a combination of thefirst selected portions and the non-selected portions. Analysis system180 may then determine a first size of the first BDD, a second size ofthe second BDD, and a third size of the third BDD, a fourth size of thefourth BDD, a fifth size of the fifth BDD, a sixth size of the sixthBDD, a seventh size of the seventh BDD, a sum of the sizes of the secondand sixth BDDs, a sum of the sizes of the seventh and third BDDs, a sumof the sizes of the fifth and fourth BDDs, and a sum of the sizes of thesecond, third, and fourth BDDs. Analysis system 180 may then select thesmallest size from the group consisting of: the first size of the firstBDD; the sum of the sizes of the second and sixth BDDs; the sum of thesizes of the seventh and third BDDs; the sum of the sizes of the fifthand fourth BDDs; and the sum of the sizes of the second, third, andfourth BDDs. Analysis system 180 may then store the BDDs correspondingto the smallest size and delete the remaining BDDs.

As another example and not by way of limitation, analysis system 180 mayaccess a first BDD representing one or more data streams from one ormore sensors 112. The data streams may comprise a plurality ofcomponents. The first BDD may comprise a plurality of portions, whereineach portion represents one or more components of one or more datastreams. Analysis system 180 may then partition the first BDD into psecond BDDs, wherein p 3. Each second BDD represents one or more uniqueportions of the first BDD and the combination of the p second BDDs isequivalent to the first BDD. Analysis system 180 may then construct

$m = {\sum\limits_{2 \leq k \leq {p - 1}}\; \begin{pmatrix}p \\k\end{pmatrix}}$

third BDDs, wherein each of the m third BDDs is a unique combination ofk second BDDs. Analysis system 180 may then determine o values based onthe second or third BDDs, wherein each o value equals a sum of zero ormore second sizes of zero or more second BDDs, respectively, and zero ormore third sizes of zero or more third BDDs, respectively. Indetermining the o values, a combination of the zero or more second BDDsand the zero or more third BDDs is equivalent to the first BDD. Analysissystem 180 may then select the smallest value among a first size of thefirst BDD and the o values. Analysis system 180 may then store one ormore of the first BDD, the p second BDDs, or the m third BDDscorresponding to the smallest size.

FIG. 7 illustrates an example method for combining medical binarydecision diagrams for size optimization. The method begins at step 710,where analysis system 180 accesses a first BDD representing a first datastream from a first sensor 112 and a second BDD representing a seconddata stream from a second sensor 112. At step 720, analysis system 180constructs a third BDD by performing an OR operation between the firstand second BDDs. At step 730, analysis system 180 determines a firstsize of the first BDD, a second size of the second BDD, and a third sizeof the third BDD. At step 740, analysis system 180 determines if thesize of the third BDD is less than a sum of the sizes of the first andsecond BDDs. If the size of the third BDD is less than the sum of thesizes of the first and second BDDs, then analysis system 180 stores thethird BDD at step 750. But if the size of the third BDD is not less thanthe sum of the sizes of the first and second BDDs, then analysis system180 stores the first and second BDDs. Although this disclosure describesand illustrates particular steps of the method of FIG. 7 as occurring ina particular order, this disclosure contemplates any suitable steps ofthe method of FIG. 7 occurring in any suitable order. Moreover, althoughthis disclosure describes and illustrates particular components carryingout particular steps of the method of FIG. 7, this disclosurecontemplates any suitable combination of any suitable componentscarrying out any suitable steps of the method of FIG. 7.

FIG. 8 illustrates an example method for partitioning medical binarydecision diagrams for size optimization. The method begins at step 810,where analysis system 180 accesses a first BDD representing one or moredata streams from one or more sensors 112. The one or more data streamscomprise a plurality of components and the first BDD comprises aplurality of portions, wherein each portion represents one component. Atstep 820, analysis system 180 selects one or more portions from theplurality of portions in the first BDD. At step 830, analysis system 180constructs a second BDD representing the selected portions and a thirdBDD representing the non-selected portions. At step 840, analysis system180 determines a first size of the first BDD, a second size of thesecond BDD, and a third size of the third BDD. At step 850, analysissystem 180 determines if the size of the first BDD is less than a sum ofthe sizes of the second and third BDDs. If the size of the first BDD isless than the sum of the sizes of the second and third BDDs, thenanalysis system 180 stores the first BDD at step 860. But if the size ofthe first BDD is not less than the sum of the sizes of the second andthird BDDs, then analysis system 180 stores the second and third BDDs atstep 870. Although this disclosure describes and illustrates particularsteps of the method of FIG. 8 as occurring in a particular order, thisdisclosure contemplates any suitable steps of the method of FIG. 8occurring in any suitable order. Moreover, although this disclosuredescribes and illustrates particular components carrying out particularsteps of the method of FIG. 8, this disclosure contemplates any suitablecombination of any suitable components carrying out any suitable stepsof the method of FIG. 8.

Identifying Correlations in Medical BDDs

In particular embodiments, sensor network 100 may construct one or moreBDDs representing a plurality of data streams to determine if the datastreams are related. A relationship between data streams may include,for example, correlations, causal relationships, dependentrelationships, reciprocal relationships, data equivalence, anothersuitable relationship, or two or more such relationship. Correlating isestablishing or demonstrating a causal, complementary, parallel, orreciprocal relation between one data set and another data set. As anexample and not by way of limitation, there is a positive correlationactivity level in a person and the heart rate of the person. The degreeof correlation is the degree to which two or more measurements changesimultaneously. These correlations may be of varying degrees ofdependence (e.g., as determined by a Pearson's product-momentcoefficient). In general, analysis system 180 may make more accuratecorrelations as more data becomes available from sensor array 110.Analysis system 180 may then use these correlations to generatecausality hypotheses of varying degrees of confidence. In general,analysis system 180 may make more accurate correlations as more databecomes available from sensor array 110. As an example and not by way oflimitation, sensor network 100 may combine a plurality of BDDsrepresenting a plurality of data streams to determine if the datastreams are related by comparing the size of the original BDDs to thecombined BDDs. As another example and not by way of limitation, sensornetwork 100 may partition a BDD representing a plurality of data streamsinto a plurality of sub-BDDs to determine if the data streams arerelated by comparing the size of the BDD and the sub-BDDs.

Although this disclosure describes particular components performingparticular process to construct one or more BDDs representing aplurality of data streams to determine if the data streams are related,this disclosure contemplates any suitable components performing anysuitable processes to construct one or more BDDs representing aplurality of data streams to determine if the data streams are related.

In particular embodiments, analysis system 180 may access one or moreBDDs representing one or more data streams from a plurality of sensors112. A BDD representing a data stream may comprise a plurality ofportions, wherein each portion represents one data stream. A portion ofa BDD may include a path or set of paths in the BDD. Each portion of aBDD may be represented by a sub-BDD that represents the data streamrepresented by the portion. As an example and not by way of limitation,analysis system 180 may access BDD_(A) representing the data stream fromsensor A and access BDD_(B) representing the data stream from sensor B.As another example and not by way of limitation, analysis system 180 mayaccess BDD_(AB) representing the data streams from sensors A and B.

In particular embodiments, analysis system 180 may determine whether oneor more data streams represented by one or more BDDs are related bycombining or partitioning the BDDs, determining the sizes of theoriginal and resulting BDDs, and indicating the data stream are or arenot related based on the sizes of the BDDs. If two data sets arerelated, two BDDs representing each data set may have a sum of sizeslarger than the size of a single BDD representing both data sets.Similarly, if two data sets are not related, two BDDs representing eachdata set may have a sum of sizes smaller than the size of a single BDDrepresenting both data sets. Two BDDs may be described as being“compatible” if the BDDs can be combined into a new BDD that has asmaller size than the sum of the sizes of the original BDDs. That twoBDDs are compatible does not necessarily mean the data represented bythose BDDs correlate. However, BDDs that are more compatible (i.e., BDDsthat exhibit a greater size reduction when combined) generally have agreater degree of correlation.

In particular embodiments, analysis system 180 may construct a BDDrepresenting a combination of a plurality of BDDs. The third BDD may beconstructed in any suitable manner. As an example and not by way oflimitation, a first BDD representing Boolean function ƒ₁(x₁, . . . ,x_(n)) and a second BDD representing Boolean function ƒ₂(x₁, . . . ,x_(n)) may be combined into a third BDD representing Boolean functionƒ₃(x₁, . . . , x_(n)). If the Boolean functions ƒ₁ and ƒ₂ arerepresented by the first and second BDDs, respectively, then the thirdBDD represents the Boolean function ƒ₃ may be obtained by logicallyORing the first BDD that represents f₁ to the second BDD the representsf₂. As another example and not by way of limitation, BDD_(A)representing the data stream from sensor A and BDD_(B) representing thedata stream from sensor B may be combined into BDD_(AB) representing thedata streams from sensors A and B by logically ORing BDD_(A) andBDD_(B). Although this disclosure describes constructing a BDD usingparticular components and particular processes, this disclosurecontemplates constructing a BDD using any suitable components and anysuitable processes.

In particular embodiments, analysis system 180 may partition a BDDrepresenting a plurality of data streams into a plurality of sub-BDDs.Each sub-BDD may represent a data stream. The sub-BDDs may beconstructed in any suitable manner. A BDD may be partitioned into aplurality of sub-BDDs according to existing BDD partition rules. As anexample and not by way of limitation, a BDD representing Booleanfunction ƒ(x₁, . . . , x_(n)) may represent data streams 1 to m fromsensors 1 to m. The BDD representing Boolean function ƒ(x₁, . . . ,x_(n)) may be partitioned into a plurality of sub-BDDs representingBoolean functions ƒ₁(x₁, . . . , x_(n)) to ƒ_(m)(x₁, . . . , x_(n)),which represent data streams 1 to m, respectively. Each of the Booleanfunctions to may be considered a partition of the original Booleanfunction ƒ. If each of the Boolean functions ƒ₁ to ƒ_(m) is representedby a BDD, then the BDD that represents the original Boolean function ƒmay be obtained by logically ORing all the BDDs that represent thepartitions of f (i.e., f₁ to f_(m)). As another example and not by wayof limitation, BDD_(AB) representing the data streams from sensor A andsensor B may be partitioned into BDD_(A) representing the data streamfrom sensor A and BDD_(B) representing the data stream from sensor B.Although this disclosure describes constructing a BDD using particularcomponents and particular processes, this disclosure contemplatesconstructing a BDD using any suitable components and any suitableprocesses.

In particular embodiments, analysis system 180 may determine the size ofone or more BDDs. The size of a BDD may be based on the function the BDDrepresents and the ordering of variables in the BDD. The size of a BDDmay be directly obtained from the number of nodes in the BDD. As anexample and not by way of limitation, a BDD may have a size expressed asa number of bits that indicate how much storage is associated with theBDD. In particular embodiments, analysis system 180 may optimize thesize of one or more BDDs before determining the size of the BDDs. As anexample and not by way of limitation, analysis system 180 may optimizethe size of the BDD using variable reordering. Although this disclosuredescribes particular processes for determining the size of a BDD, thisdisclosure contemplates any suitable processes for determining the sizeof a BDD.

In particular embodiments, analysis system 180 may compare the sizes ofthe one or more original BDDs and the one or more BDDs that wereconstructed by combining or partitioning the original BDDs and indicatethat a first and second data streams are related based on the sizecomparison. The sizes of BDDs may be compared in any suitable manner. Asan example and not by way of limitation, where a second BDD wasconstructed by combining a plurality of first BDDs representing aplurality of data streams, if the size of the second BDD is less thanthe sum of the sizes of the first BDDs, then analysis system 180 mayindicate that the data streams are related; else, analysis system 180may indicate that the data streams are not related. As another exampleand not by way of limitation, where a first BDD representing a pluralityof data streams is partitioned into a second and third BDDs, if the sizeof the first BDD is less than the sum of the sizes of the second andthird BDDs, then analysis system 180 may indicate that the data streamsare related; else, analysis system 180 may indicate that the datastreams are not related. Although this disclosure describes comparingthe sizes of particular BDDs, this disclosure contemplates comparing thesizes of any suitable BDDs.

In particular embodiments, analysis system 180 may determine that therelationship between data sets is a correlation. Analysis system 180 maycompare the sizes of the one or more original BDDs and the one or moreBDDs that were constructed by combining or partitioning the originalBDDs and indicate that a first and second data streams are correlatedbased on the size comparison. If the data sets correlate, the size ofthe combined BDD (i.e., the BDD representing two or more data streams)will be less than the sum of the sizes of the individual BDDs (i.e., theBDDs that represent a single data stream). However, if the data sets donot correlate, the size of the combined BDD will be equal to or greaterthan the sum of the sizes of the individual BDDs. As an example and notby way of limitation, if sensor array 110 comprises sensor A and sensorB, the data streams from the sensors may be represented by BDD_(A) andBDD_(B), respectively. If the data streams from sensors A and Bcorrelate, the size of BDD_(AB) will be less than the sum of the sizesof BDD_(A) and BDD_(B). However the data streams from sensors A and B donot correlate if the size of BDD_(AB) is equal to or greater than thesum of the sizes of BDD_(A) and BDD_(B). If sensor array 110 comprises aplurality of sensors 112, the optimal BDD representation may notnecessarily be obtained by combining all sensor output in a single BDD.As an example and not by way of limitation, a data stream from a rapidlychanging EKG, such as the data stream illustrated in FIG. 4, may notco-exist well inside a BDD with the output from a rapidly changingelectroencephalograph (EEG). As another example and not by way oflimitation, heart rate and respiration rate change relatively slowly andare generally related. Therefore, a BDD representing data streams from aheart rate sensor and a respiration sensor may have a smaller size thantwo BDDs representing the heart rate data and respiration dataseparately. In particular embodiments, analysis system may store BDDsrepresenting individual data streams, and may combine the BDDs when theresulting graph is smaller than the individual BDDs. This approach mayresult in the generation of plurality of BDDs to store data from aplurality of sensors 112, resulting in a classical Partitioned OBDDrepresentation.

In particular embodiments, analysis system 180 may determine the degreethat the first and second data streams correlate by comparing the sizeof the BDD representing the first and second data streams and the sum ofthe sizes of the BDD representing the first data stream and the BDDrepresenting the second data stream. The degree that the first andsecond data streams correlate is indicated by the amount that the sizeof the BDD representing the first and second data streams is less thanthe sum of the sizes of the BDD representing the first data stream andthe BDD representing the second data stream. In other words, the degreeof correlation increases as the size of the combined BDD decreases withrespect to the sum of the sizes of the individual BDDs. As an exampleand not by way of limitation, analysis system may combine BDD_(A)representing a data stream from sensor A with BDD_(B) representing thedata stream from sensor B to create BDD_(AB) representing both datastreams. If the size of BDD_(AB) is less than the sum of the sizes ofBDD_(A) and BDD_(B), then the data streams from sensors A and Bcorrelate. Furthermore, the smaller BDD_(AB) is with respect to the sumof the sizes of BDD_(A) and BDD_(B), then the greater the degree ofcorrelation between the data streams from sensors A and B.

Although this disclosure describes combining a particular number of BDDsrepresenting a particular number of data streams to determine if thedata streams are related, this disclosure contemplates combining anysuitable number of BDDs representing any suitable number of data streamsto determine if the data streams are related. Moreover, although thisdisclosure describes partitioning a BDD representing a particular numberof data streams into a particular number of sub-BDDs to determine if thedata streams are related, this disclosure contemplates partitioning aBDD representing any suitable number of data streams into any suitablenumber of sub-BDDs to determine if the data streams are related. As anexample and not by way of limitation, analysis system 180 may performone or more of the methods described herein on BDDs representing threeor more data streams by forming multiple combined BDDs that combine thevarious individual BDDs and analyzing the sizes of the combined andindividual BDDs as discussed herein.

FIG. 9 illustrates an example method for combining medical binarydecision diagrams to determine if data are related. The method begins atstep 910, where analysis system 180 accesses a first BDD representing afirst data stream from a first sensor 112 and a second BDD representinga second data stream from a second sensor 112. At step 920, analysissystem 180 determines whether the first and second data streams arerelated. The relation between the first and second data streams may be acorrelation. At step 930, analysis system 180 constructs a third BDDrepresenting a combination of the first and second BDDs. At step 940,analysis system 180 determines a first size of the first BDD, a secondsize of the second BDD, and a third size of the third BDD. At step 950,analysis system 180 indicates that the first and second data streams arerelated if the third size is less than a sum of the first and secondsizes. Although this disclosure describes and illustrates particularsteps of the method of FIG. 9 as occurring in a particular order, thisdisclosure contemplates any suitable steps of the method of FIG. 9occurring in any suitable order. Moreover, although this disclosuredescribes and illustrates particular components carrying out particularsteps of the method of FIG. 9, this disclosure contemplates any suitablecombination of any suitable components carrying out any suitable stepsof the method of FIG. 9.

FIG. 10 illustrates an example method for partitioning medical binarydecision diagrams to determine if data are related. The method begins atstep 1010, where analysis system 180 accesses a first BDD representing acombination of a first data stream from a first sensor 112 and a seconddata stream from a second sensor 112. At step 1020, analysis system 180determines whether the first and second data streams are related. Therelation between the first and second data streams may be a correlation.At step 1030, analysis system 180 partitions the first BDD into a secondBDD representing the first data stream and a third BDD representing thesecond data stream. At step 1040, analysis system 180 determines a firstsize of the first BDD, a second size of the second BDD, and a third sizeof the third BDD. At step 1050, analysis system 180 indicates that thefirst and second data streams are related if the first size is less thana sum of the second and third sizes. Although this disclosure describesand illustrates particular steps of the method of FIG. 10 as occurringin a particular order, this disclosure contemplates any suitable stepsof the method of FIG. 10 occurring in any suitable order. Moreover,although this disclosure describes and illustrates particular componentscarrying out particular steps of the method of FIG. 10, this disclosurecontemplates any suitable combination of any suitable componentscarrying out any suitable steps of the method of FIG. 10.

Compression Threshold Analysis of Binary Decision Diagrams

In particular embodiments, sensor network 100 may analyze and monitorthe compression rate of a BDD as data is being added to the BDD todetermine if using additional bits to encode nodes of the BDD orgenerating an additional BDD may be used to improve data storagecapacity. Although this disclosure describes particular componentsperforming particular processes to analyze and monitor the compressionrate of a BDD as data is being added to the BDD to determine if usingadditional bits to encode nodes of the BDD or generating an additionalBDD may be used to improve data storage capacity, this disclosurecontemplates using any suitable components and any suitable processes toanalyze and monitor the compression rate of a BDD as data is being addedto the BDD to determine if using additional bits to encode nodes of theBDD or generating an additional BDD may be used to improve data storagecapacity.

In particular embodiments, analysis system 180 may receive one or moredata sets for storage as a BDD. In one embodiment, one or more of thedata sets may be from one or more data streams from one or more sensors112 in sensor array 110. Analysis system 180 may then construct a BDDrepresenting the data sets. The BDD may comprise one or more nodes, andeach of the one or more nodes may be encoded using n bits. The BDD maybe constructed in any suitable manner. As an example and not by way oflimitation, analysis system 180 may generate an empty BDD with k bitsrepresenting the 0 edges and k bits representing the 1 edges of the BDD.A data set S^(i) may be represented as a BDD, such as BDD_(s) ^(i).Analysis system 180 may then apply a logical OR operation to the emptyBDD and BDD_(s) ¹ to generate a BDD representing the data set. Asanalysis system 180 receives additional data sets S^(i), it mayiteratively add the data sets to the BDD in any suitable matter. As anexample and not by way of limitation, an additional data set S^(i+1) maybe represented as another BDD, such as BDD_(s) ^(i+1), and a logical ORoperation may be applied to the BDD and BDD_(s) ^(i+1) to yield anupdated BDD. Although this disclosure describes constructing a BDD usingparticular components and particular processes, this disclosurecontemplates constructing BDDs using any suitable components and anysuitable processes. Furthermore, although this disclosure describesiteratively adding data from one or more data sets to a BDD usingparticular components and particular processes, this disclosurecontemplates iteratively adding data from one or more data sets to a BDDusing any suitable components and any suitable processes.

In particular embodiments, analysis system 180 may analyze a BDD todetermine the compression rate of the BDD. The compression rate may bedefined as the ratio of the space required to store a data set as tuplesin consecutive, binary form over the space required to store a BDDrepresenting the data set. Analysis system 180 may analyze the BDD atany suitable time and with any suitable frequency. As an example and notby way of limitation, analysis system 180 may analyze the BDD after eachiterative addition of data, at specified time intervals, or at anothersuitable time. In particular embodiments, analysis system 180 mayoptimize the size of the BDD before determining its compression rate. Asan example and not by way of limitation, analysis system 180 mayoptimize the size of the BDD using variable reordering. Although thisdisclosure describes determining the compression rate of a BDD usingparticular components and particular processes, this disclosurecontemplates determining the compression rate of a BDD using anysuitable components and any suitable processes.

In particular embodiments, once the compression rate of a BDD dropsbelow a threshold compression rate, analysis system 180 may useadditional bits to encode each of the one or more nodes of the BDD. Thethreshold compression rate for a BDD is the point where the addition ofnew data sets to the BDD would cause the compression rate of the BDD tosubstantially decrease. As an example and not by way of limitation, fora BDD with k bits representing the 0 edges and k bits representing the 1edges of the BDD, the threshold compression rate is when the number ofnodes in the BDD is less than or equal to 2^(k)−1. As analysis system180 adds additional data sets to a BDD, the compression rate of the BDDmay continue to increase until a certain number of samples have beenadded to the BDD. Once a certain amount of data has been added to theBDD, all the address space allowed by the current structure of the BDDwill be exhausted. In order to continue adding additional data sets tothe BDD, analysis system 180 would need to add additional nodes to theBDD, which may cause the compression rate to substantially decrease. Asan example and not by way of limitation, a BDD may comprise one or morenodes, and each of the one or more nodes may be encoded using n bits. Ifthe compression rate of the BDD drops below the threshold compressionrate, then analysis system 180 may encode each of the one or more nodesof the BDD using n+d bits. This process may be repeated to encode thenodes of the BDD using an additional d bits each time the thresholdcompression rate of the BDD drops below the threshold compression rate.Although this disclosure describes particular threshold compressionrates for particular BDDs, this disclosure contemplates any suitablethreshold compression rate for any suitable BDD. Moreover, although thisdisclosure describes encoding the nodes of a BDD in a particular manner,this disclosure contemplates encoding the nodes of a BDD in any suitablemanner.

In particular embodiments, once a (first) BDD reaches a thresholdcompression rate, analysis system 180 may generate a new (second) BDD tostore additional data sets. As an example and not by way of limitation,analysis system 180 may iteratively add data from one or more data setsto the first BDD until the compression rate of the first BDD reaches thethreshold compression rate. Analysis system 180 may then stopiteratively adding data to the first BDD and construct a second BDD tostore additional data sets. The second BDD may be constructed in anysuitable manner. As an example and not by way of limitation, analysissystem 180 may generate an empty BDD with k bits representing the 0edges and k bits representing the 1 edges of the BDD. A data set S^(i)may be represented as a BDD, such as BDD_(s) ^(i). Analysis system 180may then apply a logical OR operation to the empty BDD and BDD_(S) ^(i)to generate the second BDD. As analysis system 180 receives additionaldata sets S^(i), it may iteratively add the data sets to the second BDDin any suitable matter. As an example and not by way of limitation, anadditional data set S^(i+1) may be represented as another BDD, such asBDD_(s) ^(i+1), and a logical OR operation may be applied to the secondBDD and BDD_(S) ^(i+1) to yield an updated second BDD. In someembodiments, the first BDD and the second BDD may both have k bitsrepresenting the 0 edges and k bits representing the 1 edges of the BDD.Although this disclosure describes generating a second BDD once a firstBDD reaches a threshold compression rate using particular components andparticular processes, this disclosure contemplates generating a secondBDD once a first BDD reaches a threshold compression rate using anysuitable components and any suitable processes. Furthermore, althoughthis disclosure describes iteratively adding data from one or more datasets to a second BDD using particular components and particularprocesses, this disclosure contemplates iteratively adding data from oneor more data sets to a second BDD using any suitable components and anysuitable processes.

FIG. 11 illustrates an example graph measuring BDD compression rateversus the number of samples represented by the BDD. The BDD in thisexample has nodes that are 6 bits long. As samples are added to the BDD,the compression rate of the BDD increases until it reaches a thresholdcompression rate. As an example and not by way of limitation, thethreshold compression rate illustrated in FIG. 11 occurs atapproximately 28 million samples. At this point, the nodes in the BDDare restructured to increases from being 6 bits long to being 7 bitslong, which causes the cause the compression rate of the BDD to dropfrom approximately 54 to 46. Although this disclosure describes and FIG.11 illustrates a particular relationship between BDD compression rateand the number of samples represented by the BDD, this disclosurecontemplates any suitable relationship between BDD compression rate andthe number of samples represented by the BDD.

FIG. 12 illustrates an example method for performing a compressionthreshold analysis on binary decision diagrams. The method begins atstep 1210, where analysis system 180 receives one or more data sets. Atstep 1220, analysis system 180 constructs a first BDD representing oneor more of the data sets. At step 1230, analysis system 180 iterativelyadds data from one or more of the data sets to the first BDD until acompression rate of the first BDD reaches a threshold compression rate.At step 1240, analysis system 180 constructs a second BDD representingdata from one or more of the data sets received after the compressionrate of the first BDD equals a threshold compression rate. At step 1250,analysis system 180 iteratively adds data from one or more of the datasets to the second BDD. Although this disclosure describes andillustrates particular steps of the method of FIG. 12 as occurring in aparticular order, this disclosure contemplates any suitable steps of themethod of FIG. 12 occurring in any suitable order. Moreover, althoughthis disclosure describes and illustrates particular components carryingout particular steps of the method of FIG. 12, this disclosurecontemplates any suitable combination of any suitable componentscarrying out any suitable steps of the method of FIG. 12.

Detecting Sensor Malfunctions Using Compression Analysis of BinaryDecision Diagrams

In particular embodiments, sensor network 100 may analyze and monitorthe compression rate of a BDD representing a data stream from a sensor112 to determine if the sensor 112 is malfunctioning. Although thisdisclosure describes particular components performing particularprocesses to analyze and monitor the compression rate of a BDDrepresenting a data stream from a sensor to determine if the sensor ismalfunctioning, this disclosure contemplates using any suitablecomponents and any suitable processes to analyze and monitor thecompression rate of a BDD representing a data stream from a sensor todetermine if the sensor is malfunctioning.

In particular embodiments, analysis system 180 may receive one or moredata sets for storage as a BDD, construct a BDD representing the datasets, and iteratively add data sets to the BDD as they are received. TheBDD may be constructed and data may be iteratively added to the BDD inany suitable manner, including using the components and processesdescribed previously. In one embodiment, one or more of the data setsmay be from one or more data streams from one or more sensors 112 insensor array 110.

In particular embodiments, analysis system 180 may analyze a BDD todetermine the compression rate of the BDD. The compression rate may bedetermined in any suitable manner, including using the components andprocesses described previously. Analysis system 180 may analyze the BDDat any suitable time and with any suitable frequency. As an example andnot by way of limitation, analysis system 180 may analyze the BDD aftereach iterative addition of data, at specified time intervals, or atanother suitable time. Analysis system 180 may also optimize the size ofthe BDD before determining its compression rate. Optimizing the size ofa BDD may be performed using any suitable process, including using theprocesses described previously.

In particular embodiments, a BDD representing a data stream from asensor 112 may have a specified compression-rate range, wherein thespecified compression-rate range represents the range of BDD compressionrates that indicate a sensor 112 is operating as specified (such as, forexample, operating normally, as expected, within specifications, etc.).The specified compression-rate range may be based on a variety offactors, such as, for example, the sensor type, the sensor subject, thesensor sample rate, the BDD structure or type, the number of samplesstored by the BDD, other suitable factors, or two or more such factors.A compression-rate range has a lower and upper bound. The lower bound isthe minimum compression rate in the range, while the upper bound is themaximum compression rate in the range. As an example and not by way oflimitation, as BDD may have a specified compression-rate range with alower bound of 2× and an upper bound of 100×. This range may representthe lower and upper bound of the normal compression rate for a BDDrepresenting a particular data stream from a particular sensor 112.

In particularly embodiments, the specified compression-rate range has alower bound equal to approximately the compression rate achieved whenconstructing a BDD representing random noise. The compression rate forrandom noise (such as, for example, a series of random numbers or whitenoise) is approximately 2×. As an example and not by way of limitation,the specified compression rate may have a lower bound equal to 2×, 3×,4×, 5×, 6×, 7×, 8×, 9×, 10×, 15×, 20×, 25×, 30×, 35×, 40×, 45×, 50×, oranother suitable compression rate. If a sensor 112 is malfunctioning, itmay begin transmitting incorrect or random values, which may cause thecompression rate of the BDD to decline.

In particular embodiments, the specified compression-rate range has anupper bound equal to approximately the compression rate achieved whenconstructing a BDD representing a single continuously repeating number.The compression rate for a single repeating number depends on the numberof samples received, will continuously increase with no upper bound. Asan example and not by way of limitation, the specified compression ratemay have an upper bound equal to 5×, 6×, 7×, 8×, 9×, 10×, 15×, 20×, 25×,30×, 35×, 40×, 45×, 50×, 60×, 70×, 80×, 90×, 100×, 200×, 300×, 400×,500×, or another suitable compression rate. If a sensor 112 ismalfunctioning, it may begin transmitting the same value regularly,repetitively, or continuously for unusually long periods of time. A BDDstoring this data may have an abnormally large compression rate that issignificantly higher than the compression rate found for a typical datastream from the sensor 112, which may indicate that the data is invalidor faulty. As an example and not by way of limitation, if heart-ratemonitor outputs a heart-rate of 60 bpm for 16 hours, analysis system 180may generate a single node BDD with a high compression rate that exceedsthe upper bound of the specified compression-rate range for theheart-rate monitor.

In particular embodiments, analysis system 180 may indicate a sensormalfunction in a sensor 112 if the compression rate of a BDDrepresenting a data stream from the sensor 112 deviates from a specifiedcompression-rate range. A sensor malfunction may be indicated if thecompression rate of the BDD either drops below the lower bound or risesabove the upper bound of the specified compression-rate range. A sensormalfunction may be caused by a variety of factors. As an example and notby way of limitation, sensor malfunctions may include: transmission ofinvalid data sets from the sensor 112 (for example, if the data iscorrupted during transmission); receipt of invalid stimulus by thesensor 112 (for example, if the sensor 112 become detached from thesubject); a software error in a component of sensor network 100; ahardware malfunction in the sensor 112; another suitable malfunction; ortwo or more such malfunctions. Analysis system 180 may determine thetype of the sensor malfunction using any suitable process.

In particular embodiments, analysis system 180 may differentiate betweenBDD compression rate changes caused by a sensor malfunctions and changescaused by a subject's activity. As an example and not by way oflimitation, if a subject starts exercising, an EKG sensor worn by thesubject may begin outputting a heart wave with a shortened periodicity.However, the shape of the heart wave will generally be the same andshould stabilize at some point. The specified compression-rate range fora BDD may be set to account for these normal or expected deviations inBDD compression rate cause by a subject's activity.

In particular embodiments, after indicating a sensor malfunction in afirst sensor 112 in sensor array 110, analysis system 180 may analyze aBDD representing a data stream from a second sensor 112 in sensor array110 to verify that the first sensor 112 is truly malfunctioning. If thecompression rate of the BDD representing the data stream from the firstsensor 112 deviates from the specified compression-rate range, it mayindicate that the data stream is abnormal and the first sensor 112 ismalfunctioning, but it may be desirable to corroborate or verify thatfirst sensor 112 is malfunctioning before sounding an alarm ortransmitting the indication to display system 190. As an example and notby way of limitation, analysis system 180 may access a (second) BDDrepresenting a data stream from a second sensor 112 in sensor array 112and analyze the second BDD to determine the compression rate of the BDD.The second BDD may have a specified compression-rate range representingthe range of BDD compression rates that indicate the second sensor 112is operating as specified. If the compression rate of the second BDD iswithin the specified compression-rate range, analysis system 180 mayverify the indication of a sensor malfunction with respect to the firstsensor 112. However, if the compression rate of the second BDD is notwithin the specified compression-rate range, analysis system 180 maynegate the indication of a sensor malfunction with respect to the firstsensor 112. In the latter case, where both the first and second BDDsdeviate from their specified compression-rate ranges, analysis system180 may not be able to determine if there is an actual sensormalfunction. For example, both the first and second sensors 112 may bemalfunctioning. Alternatively, analysis system 180 could bemalfunctioning. Analysis of other BDDs representing other data streamsfrom other sensors 112 in sensor array 110 may be performed to verifythe sensor malfunctions.

In particular embodiments, analysis system 180 may analyze a BDD todetermine the rate of change of the compression rate of the BDD. Therate of change of the compression rate may be determined in any suitablemanner, including using components and processes described previously.Analysis system 180 may then indicate a sensor malfunction in a sensor112 if the compression rate of a BDD representing a data stream from thesensor 112 deviates from a specified rate of change of compression-raterange. A sensor malfunction may be indicated if the rate of change ofthe compression rate of the BDD either drops below the lower bound orrises above the upper bound of the specified rate of change ofcompression-rate range. As an example and not by way of limitation, aBDD with a compression rate that is changing rapidly may be indicativeof a sensor malfunction.

Indications of a sensor malfunction may be reported in any suitablemanner. As an example and not by way of limitation, the indication of asensor malfunction may be displayed on display system 190.

FIG. 13 illustrates an example method for detecting sensor malfunctionsusing compression analysis of binary decision diagrams. The methodbegins at step 1310, where analysis system 180 analyzes a first BDDrepresenting a first data stream from a first sensor 112 to determine acompression rate of the first BDD. At step 1320, analysis system 180indicates a sensor malfunction in the first sensor 112 if thecompression rate of the first BDD deviates from a specifiedcompression-rate range. Although this disclosure describes andillustrates particular steps of the method of FIG. 13 as occurring in aparticular order, this disclosure contemplates any suitable steps of themethod of FIG. 13 occurring in any suitable order. Moreover, althoughthis disclosure describes and illustrates particular components carryingout particular steps of the method of FIG. 13, this disclosurecontemplates any suitable combination of any suitable componentscarrying out any suitable steps of the method of FIG. 13.

Detecting Data Corruption in Medical Binary Decision Diagrams UsingHashing Techniques

In particular embodiments, data corruption may be detected in BDDsrepresenting one or more data streams from one or more sensors by usingvarious hashing techniques. Although this disclosure describes detectingdata corruption in BDDs using particular components, this disclosurecontemplates detecting data corruption in BDDs using any suitablecomponents. Furthermore, although this disclosure describes particularhashing techniques, this disclosure contemplates using any suitablehashing techniques.

In particular embodiments, a first component of sensor network 100 mayaccess a first instance of a BDD and transform the first instance of theBDD to a first arithmetic function by performing an arithmetictransformation on the first instance of the BDD. In one embodiment, thefirst instance of the BDD may represent one or more data sets from oneor more data streams from one or more sensors 112 in sensor array 110. ABDD may be transformed in any suitable manner. As an example and not byway of limitation, the arithmetic transformation may be performedaccording to one or more of the following rules:

X AND Y→X×Y

X OR Y→X+Y−X×Y

NOT(X)→1−X

X AND X(idempotence)→X×X=X;X ^(k) =X

A “→” represents “is transformed to”, AND represents a logical AND, ORrepresents a logical OR, NOT represents a logical negation, X AND Xrepresents idempotence, × represents multiplication, + representsaddition, and a superscript represents an exponent. As an example andnot by way of limitation, if Boolean function ƒ=X OR Y, then thearithmetic function A[f]=X+Y−X×Y. In particular embodiments, if thefinite integer field has a size p, the arithmetic is performed modulo p.Although this disclosure describes transforming a BDD to an arithmeticfunction using particular processes, this disclosure contemplatestransforming a BDD to an arithmetic function using any suitableprocesses.

In particular embodiments, a first hash code may be generated by a firstcomponent of sensor network 100 by calculating the first hash code fromthe first arithmetic function and an input. Any suitable input may beused. In particular embodiments, the input may be randomly generatedintegers. As an example and not by way of limitation, if input X=5 andY=7 is provided to arithmetic function A[f]=X+Y−X×Y, then the hash codeis A[f]=5+7−5×7=−23. In particular embodiments, a hash code H may bedetermined for a logical combination of Boolean functions ƒ¹ and ƒ².Hash code H may be determined from an arithmetic combination of hashcodes H¹ and H², where H¹ is the hash code of Boolean function ƒ¹ and H²is the hash code of Boolean function ƒ². In particular embodiments, thetheorem of orthogonality may be applied. If Boolean functions ƒ¹ and ƒ²do not overlap in time, then hash code H for f¹

f²=H²+H²=H. Although this disclosure describes generating hash codesusing particular processes, this disclosure contemplates generating hashcodes using any suitable processes.

In particular embodiments, the first component of sensor network 100 maythen transmit the first instance of the BDD, the first hash code, andthe input to a second component of sensor network 100. Because the firstinstance of the BDD may be corrupted during transmission, the secondcomponent of sensor network 100 cannot assume that the data is receivedis identical to the first instance of the BDD transmitted by the firstcomponent of sensor network 100. Therefore, for purposes of illustrationand not by way of limitation, the data representing the first instanceof the BDD received by the second component of sensor network 100 willbe referred to as the second instance of the BDD. The second componentof sensor network 100 may then access the second instance of the BDD andtransform the second instance of the BDD to a second arithmetic functionby performing an arithmetic transformation on the second instance of theBDD. The second instance of the BDD may be transformed in any suitablemanner. The input may then be provided to the second arithmetic functionto generate a second hash code. The second hash code may be generated inany suitable manner.

In particular embodiments, the second component of sensor network 100may then compare the first hash code and the second hash code. Hashcodes of equivalent functions are the same, and hash codes of differentfunctions are probably different. Thus, the equivalence of two functionsmay be verified with a very low probability of error. If arithmeticexpressions are evaluated in a finite integer field under randomization,then any distinct pair of 2² ^(n) Boolean functions almost always mapsto distinct hash codes, where n is the number of inputs. The probabilityof error q is n/(size-of-integer-field), where integer field Z_(p), ={0,1, . . . , p−1} and where p is a prime. As prime p increases, theprobability of error q decreases and may approach 0. Accordingly, alarger prime p may be selected to yield more accurate hash codes, and asmaller prime p may be selected to yield less accurate hash codes. Inparticular embodiments, hash codes may be repeatedly generated toimprove accuracy. If hash codes are generated for k runs, then theprobability of error is q≦(n/p)^(k). Therefore, the probability of errordecreases exponentially after each run.

In particular embodiments, if the first hash code equals the second hashcode, then the second component of sensor network 100 may indicate thatsecond instance of the BDD contains uncorrupted data (i.e., the firstinstance of the BDD and the second instance of the BDD are equivalent).However, if the first hash code does not equal the second hash code,then the second component of sensor network 100 may indicate that thesecond instance of the BDD contains corrupted data (i.e., the firstinstance of the BDD and the second instance of the BDD are notequivalent). In particular embodiments, if the second component ofsensor network 100 indicates that the second instance of the BDDcontains corrupted data, it may indicate that the BDD was corruptedduring transmission from the first component of sensor network 100. Thecomparison results of the hash codes may be reported in any suitablemanner. As an example and not by way of limitation, the comparisonresults may be displayed on display system 190. In particularembodiments, analysis system 180 may store the second instance of theBDD if it determines it contains uncorrupted data, and may deleted thesecond instance of the BDD if it determines it contains corrupted data.

In particular embodiments, if the first hash code does not equal thesecond hash code, then the second component of sensor network 100 maytransmit a request to the first component of sensor network 100 toresend the first instance of the BDD and the first hash code. The firstcomponent of sensor network 100 may then retransmit the first instanceof the BDD, the first hash code, and the input. For purposes ofillustration and not by way of limitation, the data representing thefirst instance of the BDD re-received by the second component of sensornetwork 100 will be referred to as the third instance of the BDD. Thesecond component of sensor network 100 may then transform the thirdinstance of the BDD to a third arithmetic function by performing anarithmetic transformation on the third instance of the BDD. The secondcomponent of sensor network 100 may then calculate a third hash codefrom the third arithmetic function and the input. The second componentof sensor network 100 may then compare the first and third hash codes.If the first hash code equals the third hash code, then the secondcomponent of sensor network 100 may indicate that third instance of theBDD contains uncorrupted data. However, if the first hash code does notequal the third hash code, then the second component of sensor network100 may indicate that the third instance of the BDD contains corrupteddata. If the second component of sensor network 100 has twice indicatedthat the BDD is corrupted data, it may indicate that BDD was corruptedprior to transmission rather than during transmission. For example, theBDD stored on the first component of sensor network 100 may be corrupt.In particular embodiments, if the first hash code does not equal thethird hash code, then the second component of sensor network 100 mayindicate that the BDD was corrupted prior to transmission.

In particular embodiments, hash codes may be used to verifycommunication of Boolean functions or BDDs over one or morecommunication links (such as, for example, one or more connections 116).As an example and not by way of limitation, sensor array 110 maytransmit a BDD and one or more hash codes generated from the BDD over aconnection 116 to analysis system 180. In one embodiment, the hash codesare encrypted. Multiple hash codes may be sent or the same hash code maybe sent multiple times. Analysis system 180 may calculate a hash codefor the received BDD and compare the calculated hash code with the hashcode received with the BDD. If the hash codes are the same, analysissystem 180 may determine that the received BDD is valid (i.e., has beenproperly received). Otherwise, analysis system 180 may determine thatthe received BDD is not valid (i.e., has not been properly received andmay have been corrupted). Although this disclosure describes verifyingcommunication of Boolean functions or BDDs with hash codes usingparticular components and particular processes, this disclosurecontemplates verifying communication of Boolean functions or BDDs withhash codes using any suitable components and any suitable processes.

In particular embodiments, hash codes may be used to mark and latervalidate data stored as Boolean functions or BDDs in a component ofsensor network 100. As an example and not by way of limitation, analysissystem 180 may calculate a first hash code from a first instance of theBDD and an input, and then may store the first instance of the BDD andthe first hash code separately. At a later time, analysis system 180 mayvalidate the stored BDD using the stored hash function. Because thefirst instance of the BDD may be corrupted during storage, the analysissystem 180 cannot assume that the stored data accessed at a later timeis identical to the first instance of the BDD when it was originallystored by analysis system 180. Therefore, for purposes of illustrationand not by way of limitation, the data representing the first instanceof the BDD stored by analysis system 180 will be referred to as thesecond instance of the BDD. Analysis system 180 may access the secondinstance of the BDD and calculate a second hash code from the secondinstance of the BDD and the input. The second hash code may then becompared with the stored first hash code. If the first and second hashcodes are the same, the second instance of the BDD may be regarded asvalid or uncorrupted data. Otherwise, the second instance of the BDD maybe regarded as invalid or corrupted data. More accurate hash codes maybe used to mark more important data, and less accurate hash codes may beused to mark less important data. As an example and not by way oflimitation, less accurate hash codes may be used if processing power islimited, such as for storage in mobile phones. Although this disclosuredescribes validating data stored as Boolean functions or BDDs with hashcodes using particular components and particular processes, thisdisclosure contemplates validating data stored as Boolean functions orBDDs with hash codes using any suitable components and any suitableprocesses.

FIG. 14 illustrates an example method for detecting data corruption inmedical binary decision diagrams using hashing techniques. The methodbegins at step 1410, where analysis system 180 receives from a remotesystem (such as, for example, sensor array 110) a BDD representing oneor more data streams from one or more sensors 112, an input, and a firsthash code, wherein the first hash code is generated at the remote systemby performing an arithmetic transformation on the BDD to transform theBDD to a first arithmetic function and calculating the first hash codefrom the first arithmetic function and the input. At step 1420, analysissystem 180 transforms the received BDD to a second arithmetic functionby performing the arithmetic transformation on the received BDD. At step1430, analysis system 180 calculates a second hash code from the secondarithmetic function and the input. At step 1440, analysis system 180determine if the first hash code equal the second hash code. If thefirst hash code equal the second hash code, analysis system 180indicates that the received BDD is uncorrupted data at step 1450. But ifthe first hash code does not equal the second hash code, analysis system180 indicates that the received BDD is corrupted data at step 1460.Although this disclosure describes and illustrates particular steps ofthe method of FIG. 14 as occurring in a particular order, thisdisclosure contemplates any suitable steps of the method of FIG. 14occurring in any suitable order. Moreover, although this disclosuredescribes and illustrates particular components carrying out particularsteps of the method of FIG. 14, this disclosure contemplates anysuitable combination of any suitable components carrying out anysuitable steps of the method of FIG. 14.

Range Queries in Binary Decision Diagrams

In particular embodiments, sensor network 100 may query data within aspecified range, wherein the data is represented by one or more BDDs.Although this disclosure describes querying BDDs using particularcomponents, this disclosure contemplates querying BDDs using anysuitable components. Furthermore, although this disclosure describesquerying BDDs using particular processes, this disclosure contemplatesquerying BDDs using any suitable processes.

In particular embodiments, analysis system 180 may receive one or morequeries for data in one or more data sets that are within a specifiedrange. A query may have any suitable format. In particular embodiments,the query may indicate one or more requested values or ranges of valuesof one or more data parameters, and may request retrieval of samplesthat satisfy the request. Any suitable data parameters may be used. Asan example and not by way of limitation, suitable data parametersinclude sensor subject, sensor type, sample value, sample times, andother suitable parameters. A data set S may be represented as a Booleanfunction, such as ƒ^(S), or represented as a BDD, such as BDD_(s). Inone embodiment, one or more of the queried data sets may be from one ormore data streams from one or more sensors 112 in sensor array 110.

In particular embodiments, analysis system 180 may construct a query BDDrepresenting the specified range (such as, for example, a time range ora sensor output range). As an example and not by way of limitation, thequery may be represented by a query function ƒ_(R). Analysis system 180may receive the query function ƒ_(R) directly, or it may generate isfrom any suitable query. The query function ƒ_(R) may be formulated inany suitable manner. The query function ƒ_(R) may be used to identifysamples (represented by a BDD) that have the requested values. Inparticular embodiments, each requested value may be expressed as arequested minterm, and the query function ƒ_(R) may be formulated fromthe requested minterms. As an example and not by way of limitation, if aquery requests values of {right arrow over (t)}=128 through 255, thenthe query function is ƒ_(R)({right arrow over (t)};{right arrow over(s)}¹; . . . ;{right arrow over (s)}^(N))= t ₃₁ t ₃₀ . . . t ₈t₇.Analysis system 180 may then construct a BDD representing the queryfunction ƒ_(R), such as, for example, BDD_(R). The query BDD may beconstructed in any suitable manner. In particular embodiments, BDD_(R)evaluates to 1 for all values in the specified range and evaluates to 0for all values not in the specified range. As an example and not by wayof limitation, if BDD_(R) represents a range [a, b], then BDD_(R) may beconstructed by first constructing BDD_(L) representing range [a, max]and BDD_(U) representing [b+1, max]. Analysis system 180 may then applya logical AND operation to BDD_(L) and NOT(BDD_(u)) to generate BDD_(R).As another example and not by way of limitation, the query functionƒ_(R) may represent range [α, max] and be equal to the Boolean functionƒ_(a)({right arrow over (v)}), which evaluates to 1 when the numberrepresented by vector {right arrow over (v)} is equal to or larger thanvalue a. A BDD representing f_(a)({right arrow over (v)}) may becomputed by an algorithm described by the following pseudocode:

BDD threshold(value, bits) {   result = 1   while(bits>0)   {     bits =bits − 1     if(value mod 2 = 1)       result = result AND var_(bits)    else       if(result <> 1)         result = result OR var_(bits)    value = value / 2   }   return result }

In the pseudocode above, bits is the size of vector {right arrow over(v)}, value is equal to α, and var_(j) is a BDD representing the j^(th)variable. More specifically, var_(j) is a BDD representing Booleanfunction F_(j)({right arrow over (v)}), which always evaluates to 1except when v_(j)=0.

In some embodiments, the top n layers of BDD_(S) correspond to nvariables representing the specified range. The query BDD may bespecified in terms of the top n variables of BDD_(S). As an example andnot by way of limitation, BDD_(S) may have in total layers, wherein thetop n layers correspond to n variables representing the specified range,wherein m≧n and the top n of the in layers in BDD_(S) correspond,respectively, to the n of the in variables in the query BDD. Analysissystem 180 may generate a BDD_(R) that also has n layers correspondingto n variables representing the specified range. In one embodiment,analysis system 180 may reorder one or more variables of BDD_(S) suchthat the top n of the in layers of BDD_(S) correspond, respectively, tothe n of the m variables representing the specified range in the query.As an example and not by way of limitation, analysis system 180 mayreorder BDD variables using plain changes algorithm, sifting algorithm,window algorithm, parallel permutation algorithm, optimum layer-swappingschedules for BDDs with four variables, pair-wise grouping of BDDvariables, recursive separation of BDD variables, parallel windowalgorithm, window algorithm using maximal parallelization, parallelsifting algorithm, another suitable reordering process, or two or moresuch processes. In alternative embodiments, BDD_(S) representing one ormore data sets S may have m layers corresponding, respectively, to mvariables and k nodes corresponding to m variables, each of the m layershaving one or more of the k nodes. Analysis system 180 may generate aBDD_(R) that represents a specified range in a query received byanalysis system 180. The specified range represented by BDD_(R)corresponds to n of the m variables, wherein m≧n. In BDD_(s), j of the knodes corresponding to the n of the m variables in the specified rangeare at the top n of the m layers of BDD_(s). In particular embodiments,a BDD_(S) may represent one or more sensor data sets S from one or moresensors, where the sensor data are time specific. The query BDD may bespecified in terms of a time range. BDD_(S) may have m variables, and iof the m variables may correspond to time data associated with thesensor data, where m>i, and j of the m variables may correspond tosensor data, where m>j. Although this disclosure describes constructinga query BDD using particular components and particular processes, thisdisclosure contemplates constructing a query BDD using any suitablecomponents and any suitable processes.

In particular embodiments, analysis system 180 may construct a (third)BDD representing the data in the specified range using the query BDD andthe BDD representing the data set. The third BDD may identify one ormore samples that have the one or more requested values. As an exampleand not by way of limitation, BDD_(R) and BDD_(S) may be used to yieldsearch results. BDD_(R) and BDD_(S) may be used in any suitable manner.In particular embodiments, BDD_(R) and BDD_(S) may be logically combinedby applying a logical operation (such as a logical AND operation) to theBDDs. Applying a logical AND operation to a number of operands may yieldthe logical AND of the operands. As an example and not by way oflimitation, analysis system 180 may apply a logical AND operation toBDD_(R) and BDD_(S) to generate a third BDD representing the querieddata. The third BDD represents the results of the query, and mayrepresent one or more samples that have the requested values or mayrepresent the number of samples that have the requested values. If nosamples fall with the specified range, analysis system 180 may generatea third BDD that is empty. The search results may be reported in anysuitable manner. As an example and not by way of limitation, the searchresults may be displayed on display system 190.

FIG. 15 illustrates an example method for querying data within aspecified range in binary decision diagrams. The method begins at step1510, where analysis system 180 receives a query for data in one or moredata sets that are within a specified range. At step 1520, analysissystem 180 constructs a first BDD representing the specified range. Atstep 1530, analysis system 180 constructs a third BDD representing thedata in the specified range by performing an AND operation between thefirst BDD and a second BDD representing the one or more data sets.Although this disclosure describes and illustrates particular steps ofthe method of FIG. 15 as occurring in a particular order, thisdisclosure contemplates any suitable steps of the method of FIG. 15occurring in any suitable order. Moreover, although this disclosuredescribes and illustrates particular components carrying out particularsteps of the method of FIG. 15, this disclosure contemplates anysuitable combination of any suitable components carrying out anysuitable steps of the method of FIG. 15.

Annotating Medical Binary Decision Diagrams with Health StateInformation

In particular embodiments, sensor network 100 may annotate sensor datarepresented by a BDD with health state information. Although thisdisclosure describes annotating BDDs using particular components, thisdisclosure contemplates annotating BDDs using any suitable components.Furthermore, although this disclosure describes annotating BDDs usingparticular processes, this disclosure contemplates annotating BDDs usingany suitable processes.

In particular embodiments, analysis system 180 may construct a model BDDrepresenting a plurality of health states. Analysis system 180 maygenerate the model BDD from model sensor data. Model sensor data issensor data that includes one or more specified data ranges of sensorvalues, wherein each specified data range of sensor values is associatedwith one or more health states, and one or more annotations for eachspecified data range of sensor values of the associated health states.Model sensor data may be used to annotate sensor data obtained from oneor more sensors 112 in order to categorize the data. As an example andnot by way of limitation, certain model sensor data may be categorizedand annotated with a “normal” (or similar) annotation, while othersensor data may be categorized and annotated with an “abnormal” (orsimilar) annotation. Sensor data obtained from measurements that matchthe normal model sensor data may be categorized as normal, whilemeasured sensor data that match abnormal model sensor data may becategorized as abnormal. Any suitable annotation may be used.

In particular embodiments, medical annotations may be used to categorizemedical sensor data. As an example and not by way of limitation, medicalannotations may include a “normal” annotation for normal medical sensordata and an “abnormal” annotation for abnormal medical sensor data. Anysuitable medical annotation may be used. Medical annotations may includeannotations for particular diseases, conditions, symptoms, severity,other suitable medical annotations, or two or more such medicalannotations.

As an example and not by way of limitation, analysis system 180 may usemedical annotations related to a plurality of insulin resistance grades.Analysis system 180 may use a variety of scales, both qualitative andquantitative, for assessing the severity of insulin resistance in aperson. For example, a scale could grade insulin resistance severity ona scale of 0 to 100, wherein 0 is no insulin resistance and 100 iscomplete insulin resistance.

As another example and not by way of limitation, analysis system 180 mayuse medical annotations related to a plurality of musculoskeletalpathology grades. The degree of musculoskeletal pathology may beassessed both by the number of symptoms present and their intensity.Analysis system 180 may use a variety of scales, both qualitative andquantitative, for assessing the severity of musculoskeletal pathology ina person. As an example and not by way of limitation, a user may reportboth muscle pain and weakness. A simple five point scale may be devisedto quantitate the intensity of the various symptoms. Another user mayreport muscle cramping and weakness and yet another user may report allthree symptoms. Each symptom may be scored for intensity and thenalgorithmically combined into a composite scale that could describe thedegree of musculoskeletal pathology. As an example and not by way oflimitation, a scale could grade musculoskeletal pathology severity on ascale of 0 to 100, wherein 0 is no activity level or range of motiondegradation and 100 is severe muscle pain with any movement. Analysissystem 180 may also use different scales for different types ofmusculoskeletal pathology. As an example and not by way of limitation, afirst scale could be used to grade myopathy severity, and a second scalecould be used to grade arthritis severity.

As yet another example and not by way of limitation, analysis system 180may use medical annotations related to a plurality of dyspnea grades.Analysis system 180 may reference the MRC Breathlessness Scale toannotate specified data ranges of sensor data with a dyspnea grade. Thescale provides five different grades of dyspnea based on thecircumstances in which it arises:

Grade Degree of Dyspnea 0 no dyspnea except with strenuous exercise 1dyspnea when walking up an incline or hurrying on a level surface 2dyspnea after 15 minutes of walking on a level surface 3 dyspnea after afew minutes of walking on a level surface 4 dyspnea with minimalactivity such as getting dressed

Analysis system 180 may also use variations of the MRC BreathlessnessScale, or other scales, both qualitative and quantitative, for assessingthe severity of dyspnea in a person. For example, an alternative scalecould grade dyspnea severity on a scale of 0 to 100, allowing for morerefined a more precise diagnosis of a person's dyspnea.

As yet another example and not by way of limitation, analysis system 180may use medical annotations related to a plurality of stress grades.Analysis system 180 may use a variety of scales, both qualitative andquantitative, for assessing the stress level in a person. As an exampleand not by way of limitation, analysis system 180 could grade the stresslevel of a person on a 0-to-4 Liker scale, where the five-level Likertitem may be:

0. Very unstressed

1. Moderately unstressed

2. Neither stressed nor unstressed

3. Moderately stressed

4. Very stressed

Other suitable Likert items may be used. The Likert items may beanalyzed as interval-level data or as ordered-categorical data. Asanother example and not by way of limitation, analysis system 180 couldgrade the stress level on a scale of 0 to 100, wherein 0 is the user'sbaseline stress when relaxed and resting and 100 is the user's maximumstress.

Although this disclosure describes annotating BDDs with particularannotations, this disclosure contemplates annotating BDDs with anysuitable annotations. Moreover, although this disclosure describesannotating BDDs with annotations for particular health states, thisdisclosure contemplates annotating BDDs with annotations for anysuitable health states.

In particular embodiments, analysis system 180 may access one or moresets A of model sensor data. Each set comprises model samples for acorresponding annotation of one or more annotations a_(i). A modelsensor data set A_(i) may be represented as a Boolean function, such asƒ^(a) ^(i) , or as a BDD, such as BDD_(Ai). In particular embodiments,analysis system 180 may generate an annotation function ƒ^(a) ^(i) foreach annotation a_(i). The annotation function ƒ^(a) ^(i) representsmodel samples annotated with one or more health state annotations. Theannotation function ƒ^(a) ^(i) may be used to annotate measured samplesin specified ranges with health state information. The annotationfunction ƒ^(a) ^(i) may be generated in any suitable manner. Inparticular embodiments, each model sensor data set A_(i) may berepresented as a set of model minterms, and the annotation functionƒ^(a) ^(i) may be generated from the model minterms, for example, byapplying a logical operation (such as a logical OR operation) to theminterms. The annotation function ƒ^(a) ^(i) indicates whether a givenminterm is a member of the model minterms. As an example and not by wayof limitation, samples from a particular sensor may be represented byminterms with 32 variables allocated for time and 8 variables allocatedfor the sensor measurements. Analysis system 180 may annotate the k^(th)sensor values [64,127] at times [0,31] with the “normal” attribute usingthe following annotation function: ƒ^(a) ^(normal) ({right arrow over(t)};{right arrow over (s)}¹; . . . , {right arrow over (s)}^(k))= t ₃₁t ₃₀ . . . t ₆ t ₅ s ₇ ^(k)s₆ ^(k). In particular embodiments, a modelfunction ƒ^(m) representing model sensor data may be annotated to yieldan annotation function ƒ^(a) ^(i) . The annotation function ƒ^(a) ^(i)may be annotated in any suitable manner. In particular embodiments, aBoolean variable is used to represent an annotation a_(i). Amathematical operation (such as the product operation) may be applied tothe Boolean variable a_(i) and the model function ƒ^(m) to yield theannotation function ƒ^(a) ^(i) . Analysis system 180 may then constructa BDD representing the annotation function, such as, for example,BDD_(Ai). The annotation BDD may be constructed in any suitable manner.In particular embodiments, BDD_(Ai) may be generated directly from themodel minterms and suitable annotation information associating specifieddata ranges with particular annotations. Although this disclosuredescribes constructing an annotation BDD using particular components andparticular processes, this disclosure contemplates constructing anannotation BDD using any suitable components and any suitable processes.

In particular embodiments, analysis system 180 may generate a generalannotation function g representing one or more annotation functionsƒ^(a) ^(i) . The general annotation function g may be generated in anysuitable manner. In particular embodiments, a logical operation (such asa logical OR operation) may be applied to one or more annotationfunctions ƒ^(a) ^(i) to yield a general annotation function: g({rightarrow over (a)};{right arrow over (t)};{right arrow over (s)}¹; . . . ;{right arrow over (s)}^(k))=

f^(a) ^(i) . In particular embodiments, a logical operation (such as alogical OR operation) may be applied to one or more annotation BDDs,such as BDD_(Ai), to yield a general annotation BDD, such as BDD_(G).

In particular embodiments, analysis system 180 may annotate a functionƒ^(S) representing samples of sensor data using the general annotationfunction g. The samples may be annotated in any suitable manner. Inparticular embodiments, f^(S) and g may be logically combined byapplying a logical operation (such as a logical AND operation) to thefunctions. Applying a logical AND operation to a number of operands mayyield the logical AND of the operands. As an example and not by way oflimitation, analysis system 180 may generate an annotated function ƒ^(Q)representing samples of function ƒ^(S) annotated with annotations byperforming the following operation: f^(Q)=f^(S)·g. The annotatedfunction ƒ^(Q) may be represented by a BDD, such as BDD_(Q).

In particular embodiments, analysis system 180 may annotate a BDDrepresenting samples of sensor data, such as BDD_(s), using a generalannotation BDD, such as BDD_(G). The samples may be annotated in anysuitable manner. In particular embodiments, BDD_(S) and BDD_(G) may belogically combined by applying a logical operation (such as a logicalAND operation) to the functions. Applying a logical AND operation to anumber of operands may yield the logical AND of the operands. As anexample and not by way of limitation, analysis system 180 may generatean annotated binary decision diagram BDD_(Q) by performing an ANDoperation between BDDs and BDD_(G), wherein BDD_(Q) represents thesensor data represented by BDD_(S) and wherein sensor data in specifiedranges that are associated with a health state are annotated with ahealth state annotation. The annotated sensor data may be reported inany suitable manner. As an example and not by way of limitation, theannotated sensor data may be displayed on display system 190.

In particular embodiments, analysis system 180 may perform one or moresubsequent operations on annotated function ƒ^(Q) or annotated binarydecision diagram BDD_(Q). As an example and not by way of limitation,BDD_(Q) may be queried to identify samples that have a particularannotation. The query may be performed in any suitable manner, such as,for example, by logically combining BDD_(Q) with a query binary decisiondiagram BDD_(R) by applying a logical operation (such as a logical ANDoperation) to the BDDs. The search results may be reported in anysuitable manner.

In particular embodiments, analysis system 180 may annotate a data set Sfrom a data stream that exhibits some type of deviation, variability, orchange from other data sets in the data stream. The data set S may berepresented as a Boolean function, such as f^(S), or represented as aBDD, such as BDD_(s). As an example and not by way of limitation, asubject may be wearing a heart-rate monitor and an accelerometer, whichtransmit a heart-rate data stream and an accelerometer data stream,respectively. This system may be used to monitor physiological datasteams and to annotate the data streams to indicate data sets indicatingthe subject has an abnormal heart-rate. For example, a data set in theheart-rate data stream may show the subject had an elevated heart-rateduring a certain time period. A data set in the accelerometer datastream may show the subject had an elevated activity during the sametime period. By mapping and comparing these data sets, analysis system180 may annotate the data streams. For example, an elevated heart-ratethat coincides with increased activity is typically a normal response.However, a spike in heart-rate that coincides with a marginal elevatedphysical activity may not be a normal response. Analysis system 180could then determine, based on the comparison, whether certain levels ofactivity produce abnormal heart-rate spikes in the subject and annotatethat sensor data as “abnormal.”

FIG. 16 illustrates an example method for annotating medical binarydecision diagrams with health state information. The method begins atstep 1610, where analysis system 180 accesses a first BDD representingone or more data streams from one or more sensors 112. At step 1620,analysis system 180 accesses a second BDD representing a plurality ofhealth states and a plurality of specified data ranges. Each specifieddata range is associated with one health state. At step 1630, analysissystem 180 constructs a third BDD by performing an AND operation betweenthe first and second BDDs. The third BDD represents data from the one ormore data streams that falls within one or more of the specified dataranges and the data in each specified data range is annotated with anindication of the health state associated with the specified data range.Although this disclosure describes and illustrates particular steps ofthe method of FIG. 16 as occurring in a particular order, thisdisclosure contemplates any suitable steps of the method of FIG. 16occurring in any suitable order. Moreover, although this disclosuredescribes and illustrates particular components carrying out particularsteps of the method of FIG. 16, this disclosure contemplates anysuitable combination of any suitable components carrying out anysuitable steps of the method of FIG. 16.

Display

Display system 190 may render, visualize, display, message, and publishto one or more users based on the one or more analysis outputs fromanalysis system 180. In particular embodiments, one or more subjects ofone or more sensors 112 may be a user of display system 190. An analysisoutput from analysis system 180 may be transmitted to display system 190over any suitable medium. Display system 190 may include any suitableI/O device that can enable communication between a person and displaysystem 190. As an example and not by way of limitation, display system190 may include a video monitor, speaker, touch screen, printer, anothersuitable I/O device or a combination of two or more of these. Displaysystem 190 may be any computing device with a suitable I/O device, suchas computer system 1700.

In particular embodiments, display system 190 may comprise one or morelocal display systems 130 or one or more remote display systems 140.Where display system 190 comprises multiple subsystems (e.g., localdisplay systems 130 and remote display systems 140), display of analysisoutputs may occur on one or more subsystems. As an example and not byway of limitation, local display systems 130 and remote display systems140 may present identical displays based on the analysis output. Asanother example and not by way of limitation, local display systems 130and remote display systems 140 may present different displays based onthe analysis output. In particular embodiments, a user-input sensor insensor array 110 may also function as display system 190. Any clientsystem with a suitable I/O device may serve as a user-input sensor anddisplay system 190. As an example and not by way of limitation, a smartphone with a touch screen may function both as a user-input sensor andas display system 190.

In particular embodiments, display system 190 may display an analysisoutput in real-time as it is received from analysis system 180. Invarious embodiments, real-time analysis of data streams from sensorarray 110 by analysis system 180 allows a user to receive real-timeinformation about the health status of a subject. It is also possiblefor the user to receive real-time feedback from display system 190(e.g., warnings about health risks, recommending therapies, etc.).

Although this disclosure describes a display system 190 performingparticular display-related processes using particular techniques, thisdisclosure contemplates a display system 190 performing any suitabledisplay-related processes using any suitable techniques.

In particular embodiments, display system 190 may render and visualizedata based on analysis output from analysis system 180. Display system190 may render and visualize using any suitable means, includingcomputer system 1400 with a suitable I/O device, such as a videomonitor, speaker, touch screen, printer, another suitable I/O device ora combination of two or more of these.

Rendering is the process of generating an image from a model. The modelis a description of an object in a defined language or data structure.The description may contain color, size, orientation, geometry,viewpoint, texture, lighting, shading, and other object information. Therendering may be any suitable image, such as a digital image or rastergraphics image. Rendering may be performed on any suitable computingdevice.

Visualization is the process of creating images, diagrams, or animationsto communicate information to a user. Visualizations may includediagrams, images, objects, graphs, charts, lists, maps, text, etc.Visualization may be performed on any suitable device that may presentinformation to a user, including a video monitor, speaker, touch screen,printer, another suitable I/O device or a combination of two or more ofthese.

In some embodiments, rendering may be performed partially on analysissystem 180 and partially on display system 190. In other embodiments,rendering is completely performed on analysis system 180, whilevisualization is performed on display system 190.

In particular embodiments, display system 190 may message and publishdata based on analysis output from analysis system 180. Display system190 may message and publish using any suitable means, including email,instant message, text message, audio message, page, MMS text, socialnetwork message, another suitable messaging or publishing means, or acombination of two or more of these.

In particular embodiments, display system 190 may publish some or all ofthe analysis output such that the publication may be viewed by one ormore third-parties. In one embodiment, display system 190 mayautomatically publish the analysis output to one or more websites. As anexample and not by way of limitation, a subject of a GPS sensor (suchas, for example, a smart phone) may automatically have his locationpublished to a social networking site (such as, for example, Facebook,Twitter, or Foursquare).

In particular embodiments, display system 190 may send or message someor all of the analysis output to one or more third-parties. In oneembodiment, display system 190 may automatically send the analysisoutput to one or more healthcare providers. As an example and not by wayof limitation, a subject wearing a portable blood glucose monitor mayhave all of the data from that sensor transmitted to his doctor. Inanother embodiment, display system 190 will only send the analysisoutput to a healthcare provider when one or more threshold criteria aremet. As an example and not by way of limitation, a subject wearing aportable blood glucose monitor may not have any data from that sensortransmitted to his doctor unless his blood glucose data shows that he isseverely hypoglycemic (e.g., below 2.8 mmol/l). In particularembodiments, display system 190 may message one or more alerts to a useror third-party based on the analysis output. An alert may contain anotice, warning, or recommendation for the user or third-party. As anexample and not by way of limitation, a subject wearing a blood glucosemonitor may receive an alert if his blood glucose level shows that he ismoderately hypoglycemic (e.g., below 3.5 mmol/l) warning of thehypoglycemia and recommending that he eat something.

In particular embodiments, display system 190 may display one or moretherapies to a user based on analysis output from analysis system 180. Atherapy may be a recommended therapy for the user or a therapeuticfeedback that provide a direct therapeutic benefit to the user. Displaysystem 190 may deliver a variety of therapies, such as interventions,biofeedback, breathing exercises, progressive muscle relaxationexercises, presentation of personal media (e.g., music, personalpictures, etc.), offering an exit strategy (e.g., calling the user so hehas an excuse to leave a stressful situation), references to a range ofpsychotherapeutic techniques, and graphical representations of trends(e.g., illustrations of health metrics over time), cognitive reframingtherapy, and other therapeutic feedbacks. Although this disclosuredescribes display system 190 delivering particular therapies, thisdisclosure contemplates display system 190 delivering any suitabletherapies.

Systems and Methods

FIG. 17 illustrates an example computer system 1700. In particularembodiments, one or more computer systems 1700 perform one or more stepsof one or more methods described or illustrated herein. In particularembodiments, one or more computer systems 1700 provide functionalitydescribed or illustrated herein. In particular embodiments, softwarerunning on one or more computer systems 1700 performs one or more stepsof one or more methods described or illustrated herein or providesfunctionality described or illustrated herein. Particular embodimentsinclude one or more portions of one or more computer systems 1700.

This disclosure contemplates any suitable number of computer systems1700. This disclosure contemplates computer system 1700 taking anysuitable physical form. As example and not by way of limitation,computer system 1700 may be an embedded computer system, asystem-on-chip (SOC), a single-board computer system (SBC) (such as, forexample, a computer-on-module (COM) or system-on-module (SOM)), adesktop computer system, a laptop or notebook computer system, aninteractive kiosk, a mainframe, a mesh of computer systems, a mobiletelephone, a personal digital assistant (PDA), a server, a tabletcomputer system, or a combination of two or more of these. Whereappropriate, computer system 1700 may include one or more computersystems 1700; be unitary or distributed; span multiple locations; spanmultiple machines; span multiple data centers; or reside in a cloud,which may include one or more cloud components in one or more networks.Where appropriate, one or more computer systems 1700 may perform withoutsubstantial spatial or temporal limitation one or more steps of one ormore methods described or illustrated herein. As an example and not byway of limitation, one or more computer systems 1700 may perform in realtime or in batch mode one or more steps of one or more methods describedor illustrated herein. One or more computer systems 1700 may perform atdifferent times or at different locations one or more steps of one ormore methods described or illustrated herein, where appropriate.

In particular embodiments, computer system 1700 includes a processor1702, memory 1704, storage 1706, an input/output (I/O) interface 1708, acommunication interface 1710, and a bus 1712. Although this disclosuredescribes and illustrates a particular computer system having aparticular number of particular components in a particular arrangement,this disclosure contemplates any suitable computer system having anysuitable number of any suitable components in any suitable arrangement.

In particular embodiments, processor 1702 includes hardware forexecuting instructions, such as those making up a computer program. Asan example and not by way of limitation, to execute instructions,processor 1702 may retrieve (or fetch) the instructions from an internalregister, an internal cache, memory 1704, or storage 1706; decode andexecute them; and then write one or more results to an internalregister, an internal cache, memory 1704, or storage 1706. In particularembodiments, processor 1702 may include one or more internal caches fordata, instructions, or addresses. This disclosure contemplates processor1702 including any suitable number of any suitable internal caches,where appropriate. As an example and not by way of limitation, processor1702 may include one or more instruction caches, one or more datacaches, and one or more translation lookaside buffers (TLBs).Instructions in the instruction caches may be copies of instructions inmemory 1704 or storage 1706, and the instruction caches may speed upretrieval of those instructions by processor 1702. Data in the datacaches may be copies of data in memory 1704 or storage 1706 forinstructions executing at processor 1702 to operate on; the results ofprevious instructions executed at processor 1702 for access bysubsequent instructions executing at processor 1702 or for writing tomemory 1704 or storage 1706; or other suitable data. The data caches mayspeed up read or write operations by processor 1702. The TLBs may speedup virtual-address translation for processor 1702. In particularembodiments, processor 1702 may include one or more internal registersfor data, instructions, or addresses. This disclosure contemplatesprocessor 1702 including any suitable number of any suitable internalregisters, where appropriate. Where appropriate, processor 1702 mayinclude one or more arithmetic logic units (ALUs); be a multi-coreprocessor; or include one or more processors 1702. Although thisdisclosure describes and illustrates a particular processor, thisdisclosure contemplates any suitable processor.

In particular embodiments, memory 1704 includes main memory for storinginstructions for processor 1702 to execute or data for processor 1702 tooperate on. As an example and not by way of limitation, computer system1700 may load instructions from storage 1706 or another source (such as,for example, another computer system 1700) to memory 1704. Processor1702 may then load the instructions from memory 1704 to an internalregister or internal cache. To execute the instructions, processor 1702may retrieve the instructions from the internal register or internalcache and decode them. During or after execution of the instructions,processor 1702 may write one or more results (which may be intermediateor final results) to the internal register or internal cache. Processor1702 may then write one or more of those results to memory 1704. Inparticular embodiments, processor 1702 executes only instructions in oneor more internal registers or internal caches or in memory 1704 (asopposed to storage 1706 or elsewhere) and operates only on data in oneor more internal registers or internal caches or in memory 1704 (asopposed to storage 1706 or elsewhere). One or more memory buses (whichmay each include an address bus and a data bus) may couple processor1702 to memory 1704. Bus 1712 may include one or more memory buses, asdescribed below. In particular embodiments, one or more memorymanagement units (MMUs) reside between processor 1702 and memory 1704and facilitate accesses to memory 1704 requested by processor 1702. Inparticular embodiments, memory 1704 includes random access memory (RAM).This RAM may be volatile memory, where appropriate Where appropriate,this RAM may be dynamic RAM (DRAM) or static RAM (SRAM). Moreover, whereappropriate, this RAM may be single-ported or multi-ported RAM. Thisdisclosure contemplates any suitable RAM. Memory 1704 may include one ormore memories 1704, where appropriate. Although this disclosuredescribes and illustrates particular memory, this disclosurecontemplates any suitable memory.

In particular embodiments, storage 1706 includes mass storage for dataor instructions. As an example and not by way of limitation, storage1706 may include an HDD, a floppy disk drive, flash memory, an opticaldisc, a magneto-optical disc, magnetic tape, or a Universal Serial Bus(USB) drive or a combination of two or more of these. Storage 1706 mayinclude removable or non-removable (or fixed) media, where appropriate.Storage 1706 may be internal or external to computer system 1700, whereappropriate. In particular embodiments, storage 1706 is non-volatile,solid-state memory. In particular embodiments, storage 1706 includesread-only memory (ROM). Where appropriate, this ROM may bemask-programmed ROM, programmable ROM (PROM), erasable PROM (EPROM),electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM),or flash memory or a combination of two or more of these. Thisdisclosure contemplates mass storage 1706 taking any suitable physicalform. Storage 1706 may include one or more storage control unitsfacilitating communication between processor 1702 and storage 1706,where appropriate. Where appropriate, storage 1706 may include one ormore storages 1706. Although this disclosure describes and illustratesparticular storage, this disclosure contemplates any suitable storage.

In particular embodiments, I/O interface 1708 includes hardware,software, or both providing one or more interfaces for communicationbetween computer system 1700 and one or more I/O devices. Computersystem 1700 may include one or more of these I/O devices, whereappropriate. One or more of these I/O devices may enable communicationbetween a person and computer system 1700. As an example and not by wayof limitation, an I/O device may include a keyboard, keypad, microphone,monitor, mouse, printer, scanner, speaker, still camera, stylus, tablet,touch screen, trackball, video camera, another suitable I/O device or acombination of two or more of these. An I/O device may include one ormore sensors. This disclosure contemplates any suitable I/O devices andany suitable I/O interfaces 1708 for them. Where appropriate, I/Ointerface 1708 may include one or more device or software driversenabling processor 1702 to drive one or more of these I/O devices. I/Ointerface 1708 may include one or more I/O interfaces 1708, whereappropriate. Although this disclosure describes and illustrates aparticular I/O interface, this disclosure contemplates any suitable I/Ointerface.

In particular embodiments, communication interface 1710 includeshardware, software, or both providing one or more interfaces forcommunication (such as, for example, packet-based communication) betweencomputer system 1700 and one or more other computer systems 1700 or oneor more networks. As an example and not by way of limitation,communication interface 1710 may include a network interface controller(NIC) or network adapter for communicating with an Ethernet or otherwire-based network or a wireless NIC (WNIC) or wireless adapter forcommunicating with a wireless network, such as a WI-FI network. Thisdisclosure contemplates any suitable network and any suitablecommunication interface 1710 for it. As an example and not by way oflimitation, computer system 1700 may communicate with an ad hoc network,a personal area network (PAN), a local area network (LAN), a wide areanetwork (WAN), a metropolitan area network (MAN), or one or moreportions of the Internet or a combination of two or more of these. Oneor more portions of one or more of these networks may be wired orwireless. As an example, computer system 1700 may communicate with awireless PAN (WPAN) (such as, for example, a BLUETOOTH WPAN), a WI-FInetwork, a WI-MAX network, a cellular telephone network (such as, forexample, a Global System for Mobile Communications (GSM) network), orother suitable wireless network or a combination of two or more ofthese. Computer system 1700 may include any suitable communicationinterface 1710 for any of these networks, where appropriate.Communication interface 1710 may include one or more communicationinterfaces 1710, where appropriate. Although this disclosure describesand illustrates a particular communication interface, this disclosurecontemplates any suitable communication interface.

In particular embodiments, bus 1712 includes hardware, software, or bothcoupling components of computer system 1700 to each other. As an exampleand not by way of limitation, bus 1712 may include an AcceleratedGraphics Port (AGP) or other graphics bus, an Enhanced Industry StandardArchitecture (EISA) bus, a front-side bus (FSB), a HYPERTRANSPORT (HT)interconnect, an Industry Standard Architecture (ISA) bus, an INFINIBANDinterconnect, a low-pin-count (LPC) bus, a memory bus, a Micro ChannelArchitecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, aPCI-Express (PCIe) bus, a serial advanced technology attachment (SATA)bus, a Video Electronics Standards Association local (VLB) bus, oranother suitable bus or a combination of two or more of these. Bus 1712may include one or more buses 1712, where appropriate. Although thisdisclosure describes and illustrates a particular bus, this disclosurecontemplates any suitable bus or interconnect.

Herein, reference to a computer-readable storage medium encompasses oneor more non-transitory, tangible computer-readable storage mediapossessing structure. As an example and not by way of limitation, acomputer-readable storage medium may include a semiconductor-based orother integrated circuit (IC) (such, as for example, afield-programmable gate array (FPGA) or an application-specific IC(ASIC)), a hard disk, an HDD, a hybrid hard drive (HHD), an opticaldisc, an optical disc drive (ODD), a magneto-optical disc, amagneto-optical drive, a floppy disk, a floppy disk drive (FDD),magnetic tape, a holographic storage medium, a solid-state drive (SSD),a RAM-drive, a SECURE DIGITAL card, a SECURE DIGITAL drive, or anothersuitable computer-readable storage medium or a combination of two ormore of these, where appropriate. Herein, reference to acomputer-readable storage medium excludes any medium that is noteligible for patent protection under 35 U.S.C. §101. Herein, referenceto a computer-readable storage medium excludes transitory forms ofsignal transmission (such as a propagating electrical or electromagneticsignal per se) to the extent that they are not eligible for patentprotection under 35 U.S.C. §101. A computer-readable non-transitorystorage medium may be volatile, non-volatile, or a combination ofvolatile and non-volatile, where appropriate.

This disclosure contemplates one or more computer-readable storage mediaimplementing any suitable storage. In particular embodiments, acomputer-readable storage medium implements one or more portions ofprocessor 1702 (such as, for example, one or more internal registers orcaches), one or more portions of memory 1704, one or more portions ofstorage 1706, or a combination of these, where appropriate. Inparticular embodiments, a computer-readable storage medium implementsRAM or ROM. In particular embodiments, a computer-readable storagemedium implements volatile or persistent memory. In particularembodiments, one or more computer-readable storage media embodysoftware. Herein, reference to software may encompass one or moreapplications, bytecode, one or more computer programs, one or moreexecutables, one or more instructions, logic, machine code, one or morescripts, or source code, and vice versa, where appropriate. Inparticular embodiments, software includes one or more applicationprogramming interfaces (APIs). This disclosure contemplates any suitablesoftware written or otherwise expressed in any suitable programminglanguage or combination of programming languages. In particularembodiments, software is expressed as source code or object code. Inparticular embodiments, software is expressed in a higher-levelprogramming language, such as, for example, C, Perl, or a suitableextension thereof. In particular embodiments, software is expressed in alower-level programming language, such as assembly language (or machinecode). In particular embodiments, software is expressed in JAVA. Inparticular embodiments, software is expressed in Hyper Text MarkupLanguage (HTML), Extensible Markup Language (XML), or other suitablemarkup language.

FIG. 18 illustrates an example network environment 1800. This disclosurecontemplates any suitable network environment 1800. As an example andnot by way of limitation, although this disclosure describes andillustrates a network environment 1800 that implements a client-servermodel, this disclosure contemplates one or more portions of a networkenvironment 1800 being peer-to-peer, where appropriate. Particularembodiments may operate in whole or in part in one or more networkenvironments 1800. In particular embodiments, one or more elements ofnetwork environment 1800 provide functionality described or illustratedherein. Particular embodiments include one or more portions of networkenvironment 1800. Network environment 1800 includes a network 1810coupling one or more servers 1820 and one or more clients 1830 to eachother. This disclosure contemplates any suitable network 1810. As anexample and not by way of limitation, one or more portions of network1810 may include an ad hoc network, an intranet, an extranet, a virtualprivate network (VPN), a local area network (LAN), a wireless LAN(WLAN), a wide area network (WAN), a wireless WAN (WWAN), a metropolitanarea network (MAN), a portion of the Internet, a portion of the PublicSwitched Telephone Network (PSTN), a cellular telephone network, or acombination of two or more of these. Network 1810 may include one ormore networks 1810.

Links 1850 couple servers 1820 and clients 1830 to network 1810 or toeach other. This disclosure contemplates any suitable links 1850. As anexample and not by way of limitation, one or more links 1850 eachinclude one or more wireline (such as, for example, Digital SubscriberLine (DSL) or Data Over Cable Service Interface Specification (DOCSIS)),wireless (such as, for example, Wi-Fi or Worldwide Interoperability forMicrowave Access (WiMAX)) or optical (such as, for example, SynchronousOptical Network (SONET) or Synchronous Digital Hierarchy (SDH)) links1850. In particular embodiments, one or more links 1850 each includes anintranet, an extranet, a VPN, a LAN, a WLAN, a WAN, a MAN, acommunications network, a satellite network, a portion of the Internet,or another link 1850 or a combination of two or more such links 1850.Links 1850 need not necessarily be the same throughout networkenvironment 1800. One or more first links 1850 may differ in one or morerespects from one or more second links 1850.

This disclosure contemplates any suitable servers 1820. As an exampleand not by way of limitation, one or more servers 1820 may each includeone or more advertising servers, applications servers, catalog servers,communications servers, database servers, exchange servers, fax servers,file servers, game servers, home servers, mail servers, message servers,news servers, name or DNS servers, print servers, proxy servers, soundservers, standalone servers, web servers, or web-feed servers. Inparticular embodiments, a server 1820 includes hardware, software, orboth for providing the functionality of server 1820. As an example andnot by way of limitation, a server 1820 that operates as a web servermay be capable of hosting websites containing web pages or elements ofweb pages and include appropriate hardware, software, or both for doingso. In particular embodiments, a web server may host HTML or othersuitable files or dynamically create or constitute files for web pageson request. In response to a Hyper Text Transfer Protocol (HTTP) orother request from a client 1830, the web server may communicate one ormore such files to client 1830. As another example, a server 1820 thatoperates as a mail server may be capable of providing e-mail services toone or more clients 1830. As another example, a server 1820 thatoperates as a database server may be capable of providing an interfacefor interacting with one or more data stores (such as, for example, datastores 1840 described below). Where appropriate, a server 1820 mayinclude one or more servers 1820; be unitary or distributed; spanmultiple locations; span multiple machines; span multiple datacenters;or reside in a cloud, which may include one or more cloud components inone or more networks.

In particular embodiments, one or more links 1850 may couple a server1820 to one or more data stores 1840. A data store 1840 may store anysuitable information, and the contents of a data store 1840 may beorganized in any suitable manner. As an example and not by way orlimitation, the contents of a data store 1840 may be stored as adimensional, flat, hierarchical, network, object-oriented, relational,XML, or other suitable database or a combination or two or more ofthese. A data store 1840 (or a server 1820 coupled to it) may include adatabase-management system or other hardware or software for managingthe contents of data store 1840. The database-management system mayperform read and write operations, delete or erase data, perform datadeduplication, query or search the contents of data store 1840, orprovide other access to data store 1840.

In particular embodiments, one or more servers 1820 may each include oneor more search engines 1822. A search engine 1822 may include hardware,software, or both for providing the functionality of search engine 1822.As an example and not by way of limitation, a search engine 1822 mayimplement one or more search algorithms to identify network resources inresponse to search queries received at search engine 1822, one or moreranking algorithms to rank identified network resources, or one or moresummarization algorithms to summarize identified network resources. Inparticular embodiments, a ranking algorithm implemented by a searchengine 1822 may use a machine-learned ranking formula, which the rankingalgorithm may obtain automatically from a set of training dataconstructed from pairs of search queries and selected Uniform ResourceLocators (URLs), where appropriate.

In particular embodiments, one or more servers 1820 may each include oneor more data monitors/collectors 1824. A data monitor/collection 1824may include hardware, software, or both for providing the functionalityof data collector/collector 1824. As an example and not by way oflimitation, a data monitor/collector 1824 at a server 1820 may monitorand collect network-traffic data at server 1820 and store thenetwork-traffic data in one or more data stores 1840. In particularembodiments, server 1820 or another device may extract pairs of searchqueries and selected URLs from the network-traffic data, whereappropriate.

This disclosure contemplates any suitable clients 1830. A client 1830may enable a user at client 1830 to access or otherwise communicate withnetwork 1810, servers 1820, or other clients 1830. As an example and notby way of limitation, a client 1830 may have a web browser, such asMICROSOFT INTERNET EXPLORER or MOZILLA FIREFOX, and may have one or moreadd-ons, plug-ins, or other extensions, such as GOOGLE TOOLBAR or YAHOOTOOLBAR. A client 1830 may be an electronic device including hardware,software, or both for providing the functionality of client 1830. As anexample and not by way of limitation, a client 1830 may, whereappropriate, be an embedded computer system, an SOC, an SBC (such as,for example, a COM or SOM), a desktop computer system, a laptop ornotebook computer system, an interactive kiosk, a mainframe, a mesh ofcomputer systems, a mobile telephone, a PDA, a netbook computer system,a server, a tablet computer system, or a combination of two or more ofthese. Where appropriate, a client 1830 may include one or more clients1830; be unitary or distributed; span multiple locations; span multiplemachines; span multiple datacenters; or reside in a cloud, which mayinclude one or more cloud components in one or more networks.

Miscellaneous

Herein, “or” is inclusive and not exclusive, unless expressly indicatedotherwise or indicated otherwise by context. Therefore, herein, “A or B”means “A, B, or both,” unless expressly indicated otherwise or indicatedotherwise by context. Moreover, “and” is both joint and several, unlessexpressly indicated otherwise or indicated otherwise by context.Therefore, herein, “A and B” means “A and B, jointly or severally,”unless expressly indicated otherwise or indicated otherwise by context.Furthermore, “a”, “an,” or “the” is intended to mean “one or more,”unless expressly indicated otherwise or indicated otherwise by context.Therefore, herein, “an A” or “the A” means “one or more A,” unlessexpressly indicated otherwise or indicated otherwise by context.

This disclosure encompasses all changes, substitutions, variations,alterations, and modifications to the example embodiments herein that aperson having ordinary skill in the art would comprehend. Similarly,where appropriate, the appended claims encompass all changes,substitutions, variations, alterations, and modifications to the exampleembodiments herein that a person having ordinary skill in the art wouldcomprehend. Moreover, this disclosure encompasses any suitablecombination of one or more features from any example embodiment with oneor more features of any other example embodiment herein that a personhaving ordinary skill in the art would comprehend. Furthermore,reference in the appended claims to an apparatus or system or acomponent of an apparatus or system being adapted to, arranged to,capable of, configured to, enabled to, operable to, or operative toperform a particular function encompasses that apparatus, system,component, whether or not it or that particular function is activated,turned on, or unlocked, as long as that apparatus, system, or componentis so adapted, arranged, capable, configured, enabled, operable, oroperative.

What is claimed is:
 1. A method comprising: by one or more computingdevices, accessing a first binary decision diagram (BDD) representingsensor data from one or more sensors, wherein: the sensor data comprisea plurality of components; and the first BDD comprises a plurality ofportions respectively corresponding to the plurality of components;selecting, from the plurality of portions, one or more portions;constructing a second BDD representing the one or more selected portionsand a third BDD representing zero or more non-selected portions;determining a first size of the first BDD, a second size of the secondBDD, and a third size of the third BDD; if the first size is less than asum of the second size and the third size, then storing the first BDD;and if the first size is greater than the sum of the second size and thethird size, then storing the second BDD and third BDD.
 2. The method ofclaim 1, further comprising: if the first size is less than the sum ofthe second size and the third size, then deleting the second BDD and thethird BDD; and if the first size is greater than the sum of the secondsize and the third size, then deleting the first BDD.
 3. The method ofclaim 1, further comprising optimizing the first BDD, the second BDD,and the third BDD.
 4. The method of claim 1, wherein at least one of theone or more sensors is affixed to a person's body.
 5. An apparatuscomprising: one or more processors; and a memory coupled to theprocessors comprising instructions executable by the processors, theprocessors operable when executing the instructions to: access a firstbinary decision diagram (BDD) representing sensor data from one or moresensors, wherein: the sensor data comprise a plurality of components;and the first BDD comprises a plurality of portions respectivelycorresponding to the plurality of components; select, from the pluralityof portions, one or more portions; construct a second BDD representingthe one or more selected portions and a third BDD representing zero ormore non-selected portions; determine a first size of the first BDD, asecond size of the second BDD, and a third size of the third BDD; if thefirst size is less than a sum of the second size and the third size,then store the first BDD; and if the first size is greater than the sumof the second size and the third size, then store the second BDD andthird BDD.
 6. The apparatus of claim 5, wherein the processors arefurther operable when executing the instructions to: if the first sizeis less than the sum of the second size and the third size, then deletethe second BDD and the third BDD; and if the first size is greater thanthe sum of the second size and the third size, then delete the firstBDD.
 7. The apparatus of claim 5, wherein the processors are furtheroperable when executing the instructions to optimize the first BDD, thesecond BDD, and the third BDD.
 8. The apparatus of claim 5, wherein atleast one of the one or more sensors is affixed to a person's body. 9.One or more computer-readable non-transitory storage media embodyingsoftware that is operable when executed to: access a first binarydecision diagram (BDD) representing sensor data from one or moresensors, wherein: the sensor data comprise a plurality of components;and the first BDD comprises a plurality of portions respectivelycorresponding to the plurality of components; select, from the pluralityof portions, one or more portions; construct a second BDD representingthe one or more selected portions and a third BDD representing zero ormore non-selected portions; determine a first size of the first BDD, asecond size of the second BDD, and a third size of the third BDD; if thefirst size is less than a sum of the second size and the third size,then store the first BDD; and if the first size is greater than the sumof the second size and the third size, then store the second BDD andthird BDD.
 10. The media of claim 9, wherein the software is furtheroperable when executed to: if the first size is less than the sum of thesecond size and the third size, then delete the second BDD and the thirdBDD; and if the first size is greater than the sum of the second sizeand the third size, then delete the first BDD.
 11. The media of claim 9,wherein the software is further operable when executed to optimize thefirst BDD, the second BDD, and the third BDD.
 12. The media of claim 9,wherein at least one of the one or more sensors is affixed to a person'sbody.
 13. A system comprising: means for accessing a first binarydecision diagram (BDD) representing sensor data from one or moresensors, wherein: the sensor data comprise a plurality of components;and the first BDD comprises a plurality of portions respectivelycorresponding to the plurality of components; means for selecting, fromthe plurality of portions, one or more portions; means for constructinga second BDD representing the one or more selected portions and a thirdBDD representing zero or more non-selected portions; means fordetermining a first size of the first BDD, a second size of the secondBDD, and a third size of the third BDD; if the first size is less than asum of the second size and the third size, then means for storing thefirst BDD; and if the first size is greater than the sum of the secondsize and the third size, then means for storing the second BDD and thirdBDD.
 14. A method comprising: by one or more computing devices,accessing a first binary decision diagram (BDD) representing sensor datafrom one or more sensors, wherein: the sensor data comprise a pluralityof components; and the first BDD comprises a plurality of portionsrespectively corresponding to the plurality of components; selecting,from the plurality of portions, one or more first portions and one ormore second portions; constructing a second BDD representing the one ormore first portions, a third BDD representing the one or more secondportions, a fourth BDD representing zero or more non-selected portions,a fifth BDD representing a combination of the one or more first portionsand the one or more second portions, a sixth BDD representing acombination of the one or more first portions and the zero or morenon-selected portions, and a seventh BDD representing a combination ofthe one or more second portions and the zero or more non-selectedportions; determining a first size of the first BDD, a second size ofthe second BDD, a third size of the third BDD, a fourth size of thefourth BDD, a fifth size of the fifth BDD, a sixth size of the sixthBDD, a seventh size of the seventh BDD, a sum of the second size andseventh size, a sum of the third size and sixth size, a sum of thefourth size and the fifth size, and a sum of the second size, the thirdsize, and the fourth size; selecting a smallest size from a groupconsisting of: the first size; the sum of the second size and seventhsize, the sum of the third size and sixth size, the sum of the fourthsize and the fifth size, and the sum of the second size, the third size,and the fourth size; and storing one or more of the first BDD, thesecond BDD, the third BDD, the fourth BDD, the fifth BDD, the sixth BDD,or the seventh BDD, which result in the smallest size.
 15. A methodcomprising: by one or more computing devices, accessing a first binarydecision diagram (BDD) representing sensor data from one or moresensors, wherein: the sensor data comprise a plurality of components;and the first BDD comprises a plurality of portions respectivelycorresponding to the plurality of components; partitioning the first BDDinto p second BDDs, wherein: p≧3; a combination of the p second BDDs isequivalent to the first BDD; and each of the p second BDDs representsone or more unique portions of the first BDD; constructing$m = {\sum\limits_{2 \leq k \leq {p - 1}}\; \begin{pmatrix}p \\k\end{pmatrix}}$ third BDDs, wherein each of the m third BDDs is a uniquecombination of k second BDDs; determining o values based on the p secondBDDs or the m third BDDs, wherein each of the o values equals a sum ofzero or more second sizes of zero or more second BDDs, respectively, andzero or more third sizes of zero or more third BDDs, respectively,wherein a combination of the zero or more second BDDs and the zero ormore third BDDs is equivalent to the first BDD; selecting a smallestvalue among a first size of the first BDD and the o values; and storingone or more of the first BDD, the p second BDDs, or the m third BDDs,which result in the smallest size.
 16. A method comprising: by one ormore computing devices, accessing a first binary decision diagram (BDD)representing a combination of first sensor data from a first sensor andsecond sensor data from a second sensor; and determining whether thefirst sensor data and the second sensor data are related, comprising:partitioning the first BDD into a second BDD representing the firstsensor data and a third BDD representing the second sensor data;determining a first size of the first BDD, a second size of the secondBDD, and a third size of the third BDD; and if the first size is lessthan a sum of the second size and the third size, then indicating thatthe first sensor data and the second sensor data are related.
 17. Themethod of claim 16, wherein determining whether the first sensor dataand the second sensor data are related comprises determining whether thefirst sensor data and the second sensor data correlate; and indicatingthat the first sensor data and the second sensor data are relatedcomprises indicating that the first sensor data and the second sensordata correlate.
 18. The method of claim 17, further comprising if thefirst size is less than the sum of the second size and the third size,determining a degree that the first sensor data and the second sensordata correlate by comparing the first size to the sum of the second sizeand the third size, wherein the degree that the first sensor data andthe second sensor data correlate is indicated by an amount that thefirst size is less than the sum of the second size and the third size.19. The method of claim 17, further comprising if the first sensor dataand the second sensor data correlate, then storing the first BDD anddeleting the second BDD and the third BDD.
 20. The method of claim 16,further comprising optimizing the first BDD, the second BDD, and thethird BDD.
 21. The method of claim 16, wherein at least one of the firstsensor or the second sensor is affixed to a person's body.